Ôn tập cuối năm
Hướng dẫn giải Bài 1 (Trang 99 SGK Toán Hình học 12)
<p>Cho lăng trụ lục gi&aacute;c đều ABCDEF.A&prime;B&prime;C&prime;D&prime;E&prime;F&prime;, O v&agrave; O&prime; l&agrave; t&acirc;m đường tr&ograve;n ngoại tiếp hai đ&aacute;y, mặt phẳng (P) đi qua trung điểm của OO&prime; v&agrave; cắt c&aacute;c cạnh b&ecirc;n của lăng trụ. Chứng minh rằng (P) chia lăng trụ đ&atilde; cho th&agrave;nh hai đa diện c&oacute; thể t&iacute;ch bằng nhau.</p> <p><strong>Giải :&nbsp;</strong></p> <p><img class="wscnph" style="text-align: right; float: right;" 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H6PQkH1QCiS++ygs2nmgz7og6ZEYvyi5E7S/259u3DXcVZLNbKe/dru5xxFfg5z7yIA6gRkMKPE0pwGWFvUKtBzbVQg1vYsPp5Lo9P8f/7nfz4t6Od//udPFMdi2yhDqO0TIOQWGHe2XfJ3f/d3JyEBFM7hR3zER0z3RRCqlvf/WnpQtXrl/H3BOwDyd8ZU57LeO5r3zE8yusDM2vF1lIS7B/gVBOL4xscZViJC06OArmH9fMdimDNzonxE1ajyCApjLik3B+A5BbkGgIx/X6t4GEGfu2cRAImzZ9JrDLs3GE7aTX7/e0mjj8x/2u1aiUl/5StfuXv+858/1QRZvE/5lE+ZFtMiEnR7gvF7HFhIMOFCVsM9okWEwf/FzGlLvgEBAoQI3VJkaA0AdUwZSwQ8AlJ/V0EfadpEWJQ7/9Iv/dLul3/5l6cxpgxEyBOvp+HNESsn8pPwqz4YP3pk/HaOoUt8A+Xk5s//tVGDAFVI54Cea+rvkS/RreVZDYAkdxLCm7MAAUsG101b1ahZ2Kr1A4zuhPm7akx/c3hpfkVwyn7RmJhyglwXKOCt1ibtcRZVSaIFfAiCwFcAAsIgUpSQ5khIuwVbWkjfeR6aYgwp1qux/hoOnVMU2Qv9ghe8YPdrv/Zrk2Df/OY3n7Q/f4aS0k52vVUQVWG0rvwFSgIlZA38sKLaUk4Sa1D9mrr+I0sxsgad2va5PE6Nvm9bmymQhqMJRwsdzVS1Rjfxnf+NBCj3e0aN0WcSCZGS3x/90R+dfqsA/azP+qxpwepe3wiThSYUNdRZT3fQB0LpZAlCxSKIjvAZAEsCCagSo67cvWryCFr6H3C7JnQN2FgbPywSv4OzTohdw5l1v88D5LTjuRF+AvvsZz97ElAbfz7hEz7h1EZ/19XMdaWudb4zn65lKSgAfoRIGrpoDzFaqHrUvAY8VXgrMCITlbL2EOjZJPinmMncnuCqkfugKgD6dfm7UpZ6fW2r0ocArDtcEkJ+4vBaqOc+97mTCRftsbnDfuDU/+S5KJBiOcJFiGnzlAREQCqv9xwnKqAVBEwmOYKAFoicaCv9r3VG+kw4E07NwrsWYHH1X/iFX5g4uetof/cQftzbczyfc+r6T/3UT52yt/obC6jP+qRvNrXoD74PqABbrZ7/s2Y0PB+IEKetkdX1mfkCUJEkfoXnUgCAgEKKptXxZfyjMpElSzjHIPbV3Md1/WoYtHJ7A6sD6MJaJ3fE/apWrzRoztHN9YSC5qSdnQIhgiOOLdrBcc05P6FPFoVJtzGEsDkuRQIsaflqZaIxfcZaOD9IXT0HGb0iaGgREBAEG26yqbxqec/uCTVCjavLTeg7Qedn4OWETdRKX1EYfgeQGKuozbWvfe1TQstR57j7Hu3xg/KhKpJc0dCZL79FgPB73xNk/e5KqVIu/WAJEynSN3PBf+BE87H4BnVT/ciCV6tQ6Vfn/cclwEdtZzUM2mnLGgBqh0bcL8KeyakWpIIi7bhekodAEgALJIbv1DPhO5q/akr9IzAsxTd+4zdOC/Y1X/M1k7b0/6qdqtmOJtMf2lBdPTpAa6uzBwRgI8QsTs4WSv9rGj+fAa0+81UIOLoGTACkfZQDoAHLJhURGv0wPoIXvwGIXKc/QAwwnF6WrdK+ulZOyxDpYUlEwViBWjgXy+J3pyqsBwUCBE6U0ye0TL9y+FhNoI2Ee+QLZL6XLMRRBXrf+zcDoPK3DGBkAUYdyARVjVmFvXPpU/zsnHOmUCdqINRHEC08AbCw0egRvjyHFuXYOhWO6b773e9+6vzLzkMzBkCrlsGiV0EgDImd22qIftGqub/So4xTzgFdQSts16S1aVE/IjGoxvd+7/dOFu2bv/mbJwED6PBuGpmT+uIXv3gCNG0uzp/tjNUvqdrYOABAVpglkRdBk3rlaF2rvqaerZIW+ORZ9IOiYUmtAdCa/wQZOrXpADjbqM+qDxBhGGnxfQFQBbpbgBEo8kwCT3ic/oaecMqEOsP5a6QjDrp7AYDASIDh/ne7290mWpHDoLoGIuwBT40a+T9rwuoQZllU9IiAyq4ShFCQbr20yUmXoONgA6ON6Jzf+AzCuI973OOmdu95z3tOGdzsY0af3GfswIzyAT7gcX6Tue6009/mip8kRMriyI1oN5ayUtG6lqG4iegZg37EGrLC5kL22Fj4L7XCtPohWcOR4lzT0p7vuTV4sXbPYb9f9AFGPH6kuesiVGGvNKdrhN6OvyN84eIEw/GGFkKkg/aLc1gFPm2lv7QXAHzDN3zDJKAOf0WZ6k6o9Ln6ADUkWUN8+kVjowO0NmtgPIQRKEWg5A0SMvWdPuPrAEB7skJOqcseXWPUzuMf//ipzW/6pm+aKBJwWXycn+Yn/KwGLS48S+Cqv1EVSIRZ28961rOme4VzUSDAWwJAjd5lLUKPjIVDjYLZc2we9JMCYLXMcQ4ci8BnvaP552hP6pZS5OfZAgVoKIW1VE59WKE/zfItvSKpXtgtQTW5vkvNu4FWh8vfKQc2GRZwzlxGcGgZwu/MT4KAOviHf1YeXwGa/0e74u4OicW9hQoJa98h1iewUrUK6lC0hAxpdtweRaINtc0fIdwpVyZQBFy4Vs7iLne5yxSxITh+gJRGRYFo+vvc5z6TlSKkfB6WD4D4Apx4gswPqSCta1AVDwCgjKyVOSOoqOCIAnUlF6EPCKqi0uck4DjZfBYONlpEMRl/9llUyxJlNRJYtDKgIfTmGAAoHLISHy9g0FbCyu4z30cByeqOsAh+5/uVMvi/UF8yrzRdnDODFl4UtjQgJjlUpJtvQkOoLB7uzIl0pJ84P4evc945KqY/0dgmkBChDdVSnKYFBhv1I/RdCWR3F96OYxNUXBkdQFFEefJOApEeWtxYvviLv3iKWklW+UHv1PA84xnPmATHUSXuNYdKO3B42tV9NH+lb71uvvfV35KF/Cf36U/d/1Cpyto8dEXgb9ZAVEs/AQElRU2TjAvQ9JPy83elbB0I1pl1STJS/3N+aXwi5SpARuCNjYI0JkEJSi4h7n2twpEAkIcxY4SWtiP4zLma+6TTpdxpTNpPNCbn0VQNBvW4pnbEug0IbRGHDn9d4pMdqLREdlVVLjm3+EsTFwHzO86y9gmxXANNL+Tox4LgxxYMlSEoAEAYcXHf01gsm/CoUCvNT8gpCdEev4VdCRXLwqKONrF0BVCVlPnUx9CygD9hyn3noc4vJUBbU2x8I+NntQGNNQRcNUieZdysD+U392Od0CqJSJEryi4Hd+X0D/NEyaDC5o/i8GPuYt33Ff5pTtZek9oFq/4dgaD9ZSYNwA/uzUkkuASGkDDntLBFrXU2rk+cG780Afiq+/2jMePsxknrzla3ThHSui81WnOfaMSI9lVtS8DQABlcC0griZ1LcKEdhFdfjZ+mdC+NnFAtoaYogELYkdYnSE51TqQrdLIn3roAdysQAKSEJRa7AmCL9u8WIM8xx9mBBsxoXOqK5AywANbedda9U9f6bNfQ6qJ9fCb384f4Fix58j/khBU1Z2SNdaBQhaczrq1jynWHBkCSKLQcZ4s2s9CQSnBRF5ELiyzVbpJYBJyUEAQ8Ef5kIJlKzi6+bAKqBtPpkQB3ABBME2pBaB8TBlTVgmzRFl2oRpQrERML5Xn8A7/1EzemDTmxtCVKZC4Ak1CgDrQdCqCoD/en+VE+81T3Ldck1ojKZT4jsJQSfs3aen7l/7n/lBBsPKupK7/MD98A8IFAJt04PNP4CaccgnXIVtQReLVBhlTwUgjCxqiN+SU76JaoFlbAWpozyoGSoXBqm1mnOcf7NJBstQCZ2EwCIdM5GisJKkImomEy7nCHO0xmjLZPllEbhD/amBmlOWk+jqLvCH/O9A+q+2aNOeFN34CKE/zoRz964o0iKLTqktkfCXcdc76fy1onlGrxLZR5QA09P4JA6GlNADBWi44eWlw+BYeSSac4+mucalRqNI4KAH0RPkWlCCBu7tk9bNzncW4OKlWtFqHLhHFxvCkznN46GDvfRj4C2JNJr8Kp72QB/RP14/ADAAXoB5Cxgx/4gR+YwEFGWAm0qspTV3BnBADR/H5nAS04cyQcyBowT5w3cW3at0caDIpwsBgmSzwcXcLvCEHPWm5BdNXWtDFNLPJCW8gEA1XXfHMacER9RmDIdZn4lFNw5HNol/od39P2uKqoEW1oUTl9KB9tTUj5O3yHuqj1GelvwsV1Xuv4gcx7wnBzVIxFoZw6qA4DgKW50V5qqmINWTzjNW7a2viyFTPrYTy4PiHnR5on8sOKGCOn23dCxmiVrLnyjAQGOivYIi+LFGiJ+1ZHkBMoEoLfMrUQzpGVhDHxt7nNbaY4efhrFiw7s2h+oUATQkDRhTi8ncv1xe7aKhrYZCQP4GVwJtOWSBPWNVn1KbowLM3ByIRHu4YS6QPfALenFdEfGi01RbEUrKXPbM+kJWs5dxXqgMtnteaoc3t/m1+CRAvHnwgAaOk6tl4GUZXCaJyZ51wXHyPXap8CQkGTQEONaHjjwwriJKeGSZu+pwwEDMyH0HWPmD3lKU+Z5Il/wBJkj0Pv55KlvxDo16pBR+Yvi2FROS5+6yxHhwYwELTlC77gCyYnpZYTa4/Gk6gBFILCTEK2KEJ19jLZoUABXxbdQOPwsiihWAQAtXrmM585WSCaFRXRnntqu3USO+fvY/d3LGDAE8uQJJO28xz9oNnwf9peuBRfxW1ZCSCIw5wtmQlXpp08L3kWf6MROa8ogKgbXtzLEovZ5zQIc0vgzJM10o65rsDNvBoTYOhLTZ7FcteXp6Rd86F962lsnqHPsYYsomeyyCwSLm/Mnu9z17LaAIACYg8pG+EDADSKJCcisWddE/q8SABgoDSM6A7tAtkWxkBQGh1m8rykAThMbkyV76BZ1MRnJrEf1lo5bfXwq6aPVXBthC4LmhIGgsE6xfGuXL462OH2lepUoHXOWiddO9GslYemX37rTz2ZLkeyEJratwAgZeDGE38r/XFN/axq4cwDwaOJtZ9N/5lH14R+1DmM4GcOfFcB4P4c/uXzxOiB3Pj9bR31U3SMFTBOY0djaHkyQla++qu/elJ8Gbt2yYNoIrnht+Udx+jPYx7zmOle1hxNTlIw/e/RrS38f5qDfSxANKTB4nhi9olZ0/Q6bDLE8TkzFkYGN6FPk2FBHvvYx04ODS1tIABiUJBvkEsmLABwTXXq6oKmlCLUjMNE0yYjWTV9BUS3LBVUa+HTHLnYozURJppX4ouzb45yZCHnlFlHVbIDbbSYlfJVsNa5ikX0m9YUoNAm/yPFeqN9AZUW1P7H18j3votFyhx2a5o1MV6Cb3zASCYSGBDPV6eV9c7+5pznxF9wDdngK1G0xiNAQJbqm+0r39+H+6/6AJ0DZ8DhmCI/+HsqJKEax+X0GCwHzAQYJOfWIkC7hXjoQx86RT5oDGg3QbK1/i9qARAmbhT9qcI7F/tNGBQ4AQows72vClKsUoQ0IMrfWewAZ6RV6rxEGPtcCdnlwCoLmVPbVFR6Rt5xjAZafEGAWhvT+1z70Tl8hNYzk4RioSOYI4B23l+tYJ2TXOcZNLZxWM9QpQAk2XLrTx7IAplAyQg7X+COd7zjFMlxL2vBVzJH/AZrloPLPMt4yUf2a8+907gqwc715/7ebAGqUBigMCNu6/+QSsB12qTT7DQAQeQXQCy+lxry7/iO75hivoSds8NJ4igykfgxx1UoLHtcA8YR1xtRlgxW33r9z1bTWGlApwZ1MkNzqiBWSym8KTbO4TcXgIga+D+lQZCMnTNsHikBC13LvTvou6bL/OS6GjKNUOS76ruMhKLPT/ULcr3PwvGjWPJdfBfgAMIU9Pk+vg85EOVh9ZIEY62ABUDyTONgKQVGcrbpyBLXPi+xh+F4txbDubmavx4NiJasTmIV3Ghrnz3iEY+YAMDMyRqbLJRKSJQwoCuiQhJqJo0Qdy3cOXnXWv42mb2EYASAqmHrJI1M6sgyZsxVQ/qMAOC1wsLO6+oGAAAgAElEQVQUAn+IopAsNH84MKEn/KJp6BHQUgycRCHDBAYiyBHubm2qcGatQpWq0GwBQB9jFMAW5RHLwOHnH/7Ij/zItH72UMgH0PJYA2cW0H1n/eOX8Fsi+L3ILVasAqQL9bEBYDQJPotJCj+u5jMTX7VhFaJoy0c+8pGTsAOAOvhEJ1gUmy9QKyFWeQUZYdqQFkh8fKSlKgD0jSVCgbL5HM1Y4ogdUFsWuwp85cSAJwRK8xNqVIAvJDQsMehvP/UtNoRCUozQqK+hWVkIIGFBUxWZflWhrto9/0cltKkd1rdGuyp1rOs8pwj2AYBnigoqXxAh9FxROGFe82IXHAUAAD7L/uhQaywgJ2BnjCOLNxL0M+4DdNPftU4FQ9X+Ec78fvjDHz4lNgBArD6FUvV04wgCoScEKFFKGkYJnZqhpVFQNIkTJQXCZvh1BUnCiF3jJzIUy5G4vuvmyqmrZaTBJL8AnPADHh+IMGezSzRY5/Y5poWWFBIEZEogJzvzDQChVlZqo1KkKCmCBki0rufXEvUlP2CJFs35QJl7c4rn6z/lg+oZN0orpEkpsIYAojBQ8q+exme8LEis1BzlrXKW8cdC7qO4pnu2RoGqEM8BYWSOOkhCgUSQCPa9733vSUjiQLmeAIuRi2VztjlJqJBoCWHgEPVDXSv1IoSohwyw6+3GMtmZnGyyt0A1oqIPtA/akcSRaz1fvwngCAQBu37zf9A7/daGqEVObtB+FtlzLX7CntpImJH14xdxHJVHE3rKwj9KIIVlVUA6PfXuZLkH0TUxdf5ZqOScIHdrviRUGbPnGjfhR3tyOC/tTrGhs1FwFIOaJ3kgyawcVFAtaaeTS5o+/etKbATiuc9WX5AxEvYRPVrSHN1JU6Mj5EU4KwAqyGgCgpDogN8shKgSKkGzoRMjXwAACM9XfdVXTUIj5EYTRVtwuGgpAiI+DYCEnnB6BoARHNEKtIwwWhg+Sd/s4/PQQtcRfm2jHio68VzaL/VPOXXCczi8ObWtLqZ+AB0wyamgEyJlOeaQ4GTf8EjBEMYnPelJ070EMQBYi2bNCdQcYDxHPykJ2p3VRl9leu90pzudegtl6I0ImBolc3rLW95ysgw12pW57ALdn7/29xkDwBzl6SBZ4+iPetSjpqxeABCh0k40cjQBvswacI45yjSiSXMvR1EosW+2sCgAoBaIsNgTTBDyQ5gIlUw0bSStDiiA4zkiNyiTuLPPLCotR2slnxBhsbj6aFHVqOsfgdc3gpCtiBkbWiIi5B6CKRRYD8GKEtAuwaJVUQb+gXtxbEqAVaEEaPaRn2WnmfCjcSsh3moB1jRu5jCWLOcvifEDPkAbl/FHuK2lsaClOZjXNea8UqDQtx55WhP4fWnPaQDbJwq0D7IqWCpHNRkPechDJo6MlvABAKDWt1Rakkkx0ZynbJihQVGi7BOu4TjX0kaoj2tCgWKJCB8hP++88ya+nhOVAYfjyjoB1e1ud7tJi7EUgCA7GRqU8WmLgOK2zL84PoEztlC7jN+4+AUiI7Tnl3/5l09WoFKabi3jgySixMLg2QGBaFktB858OROJBfB9ABC6NbKa9bMRCOraJ9Rp7BQIZaYg0pxF+Pk7NfJn/oBYqQMQUybA2QEwcsqX2EVlDSMKtyaze1Ggtcb691n4vqj3ve99J0GjxQKAHt/NveHN0Qomz2TTJCaUgGtHTJlwmlALxFo86EEPmpxnMWdaPv1IxSIAMN20FboickSLcdD5GF/6pV86CVfClkx2rWvKTiaA+b7v+77JpKt/QreqZo5QEqycFOEzABDyrBagOnVVcZhbQoQKApBomb7pdyhRSh6AxllErJnCMk5wNu1X4a4O9JyD3627uU2iK3F+FtK8m0fhztT4VFC5jwVQn+U+c9ud4DreNa2/xEb2sQh7OcH7NFxNeUW1/9/vfvebCuYqALIYXfuMrEEEgTbMTjOUiG/ASSQItHleoI3L5zgS7Wf75bnnnjtFK9AdQMq7Bgi8v4XqCFmKv5j0WmtEE0v0oDS0/e1vf/vJrNejCjOetMECqHcxrgCg7pGuQlnnLX6GdmINsgMNFdJfEa8kHPkaqF4Ng/Y5znrGAV9bX31gXc0fPwrt+aEf+qEpSVX3cSR+PwKAIki07su+7Msm4Na941WbbwHAnC+6No5NFGjJ0Z3rXL+nW4AM8MEPfvBEF5hnB0Kl/qcvRNWcdXIsBGHFu3F5liAvvKDxc1RHQpp1J5J2YgG8QYbG51yyECwADq9tmkx9U2rS3Zf8Rl7SjcZxfGl7AsACZC9Drk+/A4Ac6U4jogGEd84CVCUSn8NvAihAAIBAnjdhJouuTXOaPtSjE2NJ+xqOMqzdopv37O4DZAoIeOPs5/CB5Dc6bWIB1IgBAPBTWj2kPSe8o89PDAAjXrYFZdWkVRoEAIQHBwwAanJmxFG7eQw3RolEFzh8gMBZ5VjSiOHXlftqOwBgAdAEgAFGjhpAaYvQ2NYpGoSjRwOzLCkEJICccIkewMsBsp7RE1WxZDgzofW35+Z4wyXePVIs0cY0PedYn7RNoFAL2hV4swd5pO0zp3W/xhLNBVrzRXnxi1BAB/mao+z/9rwa1AiIQ4ECAIcabwXAnKxdJACIJtoKgO6k6PQDHvCAKU6Om44AUJ2ZKviVDuWaxKEBQdhQ9IeAEXrt08ooUI4xtNiVAtFoBFi8XlsWGH+2yHiq3UeENJqXoOHgnpHadtYjr0Sdmx/zRQhyRpJxoWp5SV+dzyVtVxVJImVASfgJpX6zhhQATg6YOYQgIKvOqf5u4f+xnOibUCZBN298LzVbtH5OcxsBIPVjAGDO1wCwj3x10G6595SMbUmEdaStPSBcc+SoWLQAgA+wBIDugHWnsLbvOwsABKwLHwNF4gTSUrQtPp9NGyI3NmDjtL5HeQgnSiM8CkhqzxXr0W7oEQtj8V3DyogKEf4kehLrnwNBpXRL/HtJ442squsJGF7OgnHiAVm/azlFtVD6GIXSN8x3gUq0hwOvbc+jXKxf3l2cI3CAK5Sran/9synGqQ8AgAJRTj2EHZCuyVhXrLXPW+49VgB0itQBUDtr0u9///tPDtRSFGhO+MNhKyeOYGkbCAg3x9S+g9TbEwQaG9/PK1QJOmvAhAMIbk+4aXc/KBBNmvN9OLx8BEVqOa0t/kutsx8BIMLmeUn3h570YrURDamavwcV8nd8I0pAIkykiPVC79ANodP6Qg79cG/CtXP0B80y9nB+CUH01Vz6SZ3R3NoQfv/4KqwnAHCCAaDu9qvzto8Qz/V7y+ebokBrFmDkI8wt4mEBEHOv3ZjwqkXjE+gLrS5U+vVf//WTqRYZUoWpqA4IgIIg05Z+OI+iJwDAamhLeFJEhzbDsWl+voFIC+EHjJj6CHClaJ3Tp9rR4qMrfuQMclpD/Iau2eoYKwjq/GZuXBsl8IQnPGESWoJn/MaIriRAQPD4PNpMjVLazJlCACKShPYJO7uW4Bs72hPLseRAuyehU1YJheLAo0ABQNfeS/7QFqHe55q9AVA7N9JK+X4ONCaDBUBRmNGaCKtaPYOIya+LXKsE873fFi4+AXMtLMkZ5BTiySIXIhWsAQqDG1ft5d6U4iaODyTqV/gsFkxJcxze9HFOAGIJq4YGInkDPyhUXu1UTf+cczeigHlGVRA5FUKImPCzAvwDFEnfJatSZo629eQeRYDyASpFItzK2beJJUWFW4WsAiBRIACwJZIyqvt60+ZZD4A5ehLtPKJAdaEAoCbCRgfm9md0C1CjRr6LBXAfzWbx1aMQfhldgoYS0GSSXzS5DKkFRQHSfs1IC5Fy2tAi7UiocahDGepCZXxVY3choVGBEPXyPE42S1PP/az3j9qq4KBMUt/jWdG02lYKIeSK3nHwaXLCjMaIavF75E3iwOYQrsyDDDmgsiIsp3Ju1Kcfa1kV1RwoopxYUvOpLwFA/KZKec5qAFQtXTVb+N9cqW0HgMXgeDpHtANgpAGrph9ZgFCHWAAOq51ntLbCKwJP8zDnHFwOGc3HD8kbWeKQZS8BvooqsRaiQeLr9Rjw9NPYaLJQoMxFVQQBqaypdl2DBwvVVgBkfl0/4sGd/9f1iPCiPUozZI056QRdW4SaNtcH7RhXXnZhLozND0vBQuf9w3IcLAcgzJ3xqb16MECUYfrrOwCwFxwAWOdsiOkCf7ECQBXM8NiRBYh2sEiOAkdRaCY7wmotTOfA3RJ0M+n5EZb0hSbEtWlw3D5Hd/tekotQE4K8cohTix+7zjXAQVPmeHFFcZzImlAK385C101A2uihxgDAuFkA3zs3CajqzqcIfcA0opxd03bfwL2y2cq9CTbaZ06MPYWAFAFB58cYv36gRTnWxtx5tlCqSBrNn/0InZ7m7wAgY69z4jtKCQD0y8mBFE+c4LPaAnSh7I5ZBK9r5iqs1VoogVbrzwx7cUQyh0v0YWReK8fuViOUqCektCOsJxuJj+sHrkuzEQLXWyjgQJtyQvMcTalWoGrj3t9sIUVLRKiYfly8vgyv+gFdyDI3HRAVKJ2O6FvyHng9IUTfCLlcAWqnP6JiQCBKBCTmhFKi+dGeFKwBSy1fNqZsZ+w7zroSqADQFwBgVeID9EToyPrNUayjfL76jrA5oaxaPgCoC9gF46QA0ME5EqSAg2OctzWmnAIwhP04kvwDTmROIehgynirBvZZPWwqz482rO9RALi8wjRbTEcZ5Ah5+H6EJeHFPLNaYP33N0F2Ha3rx9+JSLkGLQIEAsxS+F50SujUPxGirG9KSjImQDJf+pOQrrHX6FCUZyiQYjgAQIFYgNHuvrOCAmVBlgAwR1eWuKvFZAFEJWIBerp+iQZVq5LrOgCzoUSJhI0uMd21X6EkrIEsMrrDQeabuI7JzxtPotmjrUK7/B3NF8vidwSgUoK8UA7oaE2CkrfFp4I1zwmgIqg+D80jbDksS99dW2mEZ/sejaPN0RpC7JnG5dqclgHY2hUUMAeEWWyfv8N5ljPQxwDI9/6vD8lqA5YoE+CgV6yEkHMy3Fmb6gO4BwBYgGpROr09imbfeu+sBaib3kecvgt5HL+lB0dw+ADMrCIqu7UqACqtmaM99fNMcNX0FpsASAbhr1L2qIafzs19ZnH4DMoIOI+0vvCpCtJ6fXyAgIewReD023P1J6DIER8EkrAlCeaZcZq1T3jq/FVnNlq9hoFDa2hg91dgpo/qnDjBBFkEKyfQBWyhR9olkOYLNaMsZGk5yK5xPcGnsNAlP4QWuHxuTNp3HyUiXCpilJd61LEkDMoC2K2Xl4V0WTprLEA00kijH8YyaA+wAMCEAoDdWiMArCG48/9MNIGgiQiz9wRz4sSvJW86ZYkFca/Ij9AsK8DhtYjZaDKnmeocdCUx+rta1SrwBLpz+a5Qqo+Ttis1qn0EjO/+7u+eqI3xc+Jx/1qlWTWzsfN5OOdAL9xLiwN0nGKJQPOhPUV2Tp0wx8LNfBn+A5+KxbEnQo4l4/KsFNJJhLGCQtMoYC2bqIJ/kfsAtGIFwL6o7E5pFigAEJNHgfYFwMjyZDHzTOZcCA8AOLG2Rsrq1vF0y0ErifxYaGBxagFOHKsxcnZHlrFaogriUBihWPX8tHbevF4z27Vf1THsbdW/65y4n1a27ZTGNcfKumWc6ws38hzrIW9CeFk/16l/EhEjqKnfyVk+LGreVCmaBmjmS0hTVMmc8R0CtigmzwFItUCeBwBA0wGwpHTXlOJhvl+kQOnMXKf2EYAKAD4AAIgy2K5YN4TUQVTBmBtcF37XWSzaSYSJxnI6BAAkMtGtl78DGokf18od5G3tXdNXbVv7NQf62se8b5gwykGkpGAk7HO+VLcGfTx8AwAgcBSAhF9elFevDSUlkOgNC+A6ABAVMic5sBbPVxslMhbqR+A5tY7ETEUsOpcT/TI3QBAfwIYYwOIDCD2ftU7waDFHXG1O480JBk2g/IHGQTMAYO41l3MlBr3tUIFQmlAgtUDKLQIA3/fS39ybt1Pa3yo5RGiY/KoE8v8ugHnuCKQR/mhCSTialqCgGgRqlAgbgSwCW7/rwPEcAuY0ZRYAAFCUesJc+mstXI/qUEjoCQqEwgAAv4hfoL+EVeZahCj7K/gBAE3bE/pkyBMEqDQ1YVCZ4BoFSia4h0HnLNxhtPzSPUfaE7zG0yIoVWBMhNPg1NjgpgFA72Qo1wh0tb3wy4QZ/U2YZTK/7du+bRJmZc1CbnEoa5sRTNoOBVJKzYQ7wz7v9F0C/tLkduEncDSq2iIAiEbtO8KW6E21JgmL1uuTBLRVUVUoBzWnc9dy7cyb9YgFcI+IEQsgaCBXwCdCC1lFjqsAgZ/Mdxz9gKIqjJoIcx2wsABxgq3JJQ4AFigAYAFo5zUK1AWiA6D+TaBppuzXxTNFdPK+qZFVcQ9tBwDq3YFGxWfd23sYjdTpmbHLQNOorJ5McD0Et1ub/ndtT59z0FUHgKiOvIYxGbeITk7e6Babk5u3wOPnQK9fojmyyRQCAJjDACDznegZ4RYyrsdPBiSxNgEAkHUAhJqOrN7SZ8dhDU7UAsSEj/IAVTv1Qc9x4UxujaBEs9FqHE6a1uL3MoYqCLEaKj45z7Rd3qvlut63pahYpUPd0SYwAPDCF75wAoDKUhRoVAoxAkMFQIRmRIH4AErCzYG+Gn82w1Sh0QYAsH4ssheXEGSWCQCUhosOAQYfQAGb4r1QG1RL3kQf+AByCHVuagg5AAgFAqbUAvWxrs3vcQj+KRk7yrlA+1KgCGevBVqrBl0DQIAV2hRak4mt93dqlWtpJY4zAIhqiJywAFWTbdVQlfrV/3uW8C8/g9DnnbfHBYDMQ8ou/PYPgBNq7gDIeax8Mmf2sADKtBMGlSRz4JfsuMgYemi9tCsU6h5WTIm5EGgPZWb8gIYCxQKIAl1iABCtWAEgfixBdY973OO0HUldWOfQ3oWs06IeuRmBQNtJaomF8xtEgSwMCqSQ7igAqEDUDqEROXHSHaHMGyPrlsSl8XdKFZ8mc8TC0P5+1/Jm19WMdbV++mTsiuOMnaXkm6mezandmRft5qDbnF/KfzFXLMDoBO70GdBEpTjanmdDTPUB1tZ9Tdke1iocOwWqgtj5ZgDgYCxVkQCQatBaSLeF981pWfeabOabeaaVshWwtpsJDQBYANs0kwizqD0MOqIlo77OgdPn+pY6ndCy/g6Duph14Tulqto240Z9jEWNEzCgJbT56KgS7eWldiJGDgPwI9pDoFPTlL3GrBe6FFooYsRfQovyeqfep/Q5YVAWgI8iMLG0IaYL9MUeABEKAocCKbcFgK/7uq+bePpxACCWhhBYLFEgURDn76i7r5SoAkDfLEp8AA4fCjQCwJym6YKavlTrN6cc5k5l6MK0puUAC+8npPg8JaAUQkVnXpOUNmKdgIQ2x/VFaKyDyBzhTC1SgAJU6qtwfwkzkSL/5rK5dex9P0B8gByMNZf026IM1+Zl6fuhBag3jBZtCY1V+0XgquYy8bUcWi3QCABriF+iQDQgs60EwqYb2WaCkP6MKi4BQClEjm2XpNvHAozmrPfR2AlpCtNyzOJxASDtoxgytCJhhJ9DL+tcT2CI5SOYwsYsMu3MGpmvACDr0H2nCvCRZa3W3zzUPEA2xNRTIc46AIwEf8ksdQ7er833NI5EGIfIiytsWwxf7Q7UEnK7c1mvJcxCmhJhMsEWNC/K7rw5C2lRWACJH2Z9zgleA+ac5k8phNi60xEIWo54Hx0NUq3VVg3nGanRdyKGUmdOqzwAMKdormrmvMhOIgwFCgDy/q45wUwkaEs/A0x+hsyxMHW2RFbLvzS3W+Z96zzV647NB+iav2vEhCpFA5wFZDJoJnU6vRguk7oVAIl++G2iAIAm52CjWUw6AOT7Ti30Ldljb1ZJHiDFcEtZylEfR9YpdAI1A07aXxSIj9LP0anadp+FT8kBbfu4xz1u2vnmFAdOrbFUAAQEhDFbRZVCCJkSTuDMfFVLPhpvtRIjxTcCgFIIFuCsB8ASBVrivR0ACc1ZHBRI2C2Z4KNSoIArfY0wO4BLeA4VMtkVWLXv7geaJH1SChEKtC8AuvmvAEXNkgm+7W1ve+pUiJo1HVG1LdrNHJtf4wEA5dAokIRjaoH6uqBkKCNgitDkkF+bgbQzV4+1FZgZu+fEAvBTgOysB8AcDRohfokC+a7uQhIFMuEW5rh8gCxsMsFCbpw6ESAUIPsBRlEK9wKALLCsZ14rNAqDbln4PhfxgfQNzUI1gF4oUM1NtQCVntTygi0AyH4DPoVcAyeYJk8FZ8+CRzhzZIz50hdWWdDguADgOfom2WZPMABwgisAlnyALXO+ZX6G1mspEbYPAKrWqzxY5xNxyESIAqk+jAWoe4KXzGnXXlVYal+zg0nUQrSCA0izjfhqtRrHZQE6HawKQKhVhMaYhQKVKSQSEl4d6rH1zM7MS84d1bbQJUHzf4krNLMnw9IvALBBSZbWD6UkDLovAKpf0K1gLIBnpBw6e4JH0a4zKfSbfYAlR7h2cIkK1UX1YIuEAgUAHNTRS9/WJmDEs6sVqNsJa83MyAJoKxbAG+xjAaT/R9GP3re5eQo106/0R7RFwonjKzybg7Eqz66O+to81MUkWOhMTqzTL/Ptn0DDqB5IHysAKA9l5KyG+5fKtHvf+lpXEPD9UCBWht/BAgBAQN6fs8+4D6v9pzk/jAXIA9eoULcKAQAnmMZBgeQBUgoRIai/5wbXAVDrgRLiy4JU0z+iAZ7Bb0CBpPbVAikJzrsBOmgOA4BYwbxDVxsc8/o2lapB99X+xgAAxlHPLiLQ9dTmHgkKZZSXQU9ca00I53EDQIGeUCvAAYBMcNbjrAJApTAjIV4CwIim1M/EwFkAJ6SJtQtV1sNZt1KgbmJz4KwFzi4ndSzAxQFMvc2oGjQWQHRGJEQtkJJgNe4jC7CPxqnlENVZ98wIeep1Qhe1X7PDW59H07MA5oKWJfwoIIrlebK1NeQa38S11gMArI/sPOGsFKgrpRFtidx0CuhzFMieYYV1+lgPx+3jm2t76zzsc91sIqyb9ZGZXxPW0T0mmAVABfgAxwGA0IsIUDLBkkFMOWHOmZajjLN+0pwAwEFlAdATAPAzAs2WSR4JQmL1oTld0ydadhgAELIcfqXiVLEaQeZsAkLeWJl1qwBgkcXoWZEAYM4CBAwjmlJpX/fLAMCpeOimcoulWqCLlAKNLMDSgs91diQAtFQAwAKY7BwxXpG/dQISyaiTzcQKN9oTjM/nhdkRuu6zVB8AAFiAAGCrBZjzAyJkESba2RxoN8eiVPOf6w+jBUN3jN/rn+znBWb7ggk/J7jnHDyP0ANAIjQoEOHclwKRkWrxAhTtAKd6IxZApjrvB5jzsbau/xZFtCi7Ix9gifbUxtY6uQYAPkC1AMcJAKXNeT8wp65viu8UilnmA4QC8QFCgeZCdFusZAWAZyorttHEj9Bszus/6kK6H7hYWELoNalCwRJhstp5d1m1ON0CBADWZASAut5za78PAKoP0Ntek63jmK8JoEsAOOpD5gDQfYC6H2CNVvU+xQJUgaZhsinenmBAoNXzM2cBhEG7DxAKNJqLPr6RFchnoQaEUt9YAcfC5MDdo861+2ly9ELo0+nQyk1svJdxd0xJf3tj5g5t4gSjQPEB0KZuAbYAoAM+jj3rJDMdCmTXWd4P4J5LFABQoJETfFgLUAXP/wFAwonmz6Z4FZ4j7poF6xYgTvA+AKj8twp0BamaG0KApuDBhKBvJTwsGAiySlA0x3uLUY4Uw+VYlDrHIwAA5pwP0LXySEt3AGQsAJA3xPC3AKCeDdoVX1dSc3NyVEtxohbA5JhgiTAbYqoP0J3TrQOrWjiTTxMStEc84hGTKSfMatZHAPCZ+3IuEAuQMGic4KW+RIiysSTnKWUXVrRuqIEtkUKB6Epi4WcCADLBSpcVtSmIA4D+LrARBWIB5nyALQDIfFalFMc/FsBcBwBbNsUvcvhzzjmsvjiQh5OgQHVSAECNjuNBcjy6xTksANJ2DTESQlxbpEmc3e6mbHAPCLqGTgWpOp2cCxQfIM+Yo0GeJ/Ik0eO4QH0RcrTjSzItoUfXyQSruRHlUQ8jSlVPhTjKarIASYSJALEGnF/5jLzFsmtWfY3C4ANoYysAlvrarXKnQOqg4gN0xbRV+Y3Wct/5O3EA0HzeEON4kOwIOy4AVGuQ/bA+I2x911UmOVpwCQAjbp+JjlVz2htqw7IBucUV5mV5kukGEvxfiJLWVwrh+5w+ve/i9euz14DVyZk/xpmaorkcCKFXm5UwKADEBxgdVrDWzy78rg8AgN9cA4Bn1Pb39f8ulgAgHPe73/2m0xFiAZK6P4wPUC1ABQDNNnfSROfBlQLJBHOYaxRoZAGyWDHvqIMxuR/ICT/qwRIEfKySEhDCBvSuYSVGJySvCdno+/SlC0Yc0REFNHZ9r3mAowKgzlfWBACSCOMD8H9kwrNGWxzs0Zj3sRbD+y8KCsQHICyiIGL1c+/c2iIENcqSaILfzDqtTLt2B7BPmutTC5REWM0ELwEgFoTGta1QsReQO1oxb5n0PMJpvzHn3E4ttMR+AGHKvJBvy3iXrgkA9An9AcQcCxPQVy2bvgNALAArJQxqR5jv5yzAyCpWoHUQ5HBc/g8AyAQDgHu6ZVpzgA8LlosMAHWyUgqBn8cJPioAspCZdAtPyCRdxNpFgmwM9zNXC5RNNDURlvfg9oWtGjZOMOFT64JGAAAAAUDO4wdGTrlsswOr7DWQoHI2ECqQt7AcBQQBAG0rEWj3mWpTpc2sTHU4qwWLD6DvolOiQFsAUBVOF9q6JsYEAJxgAABOAKiRuSWqVeWnWu+LDQUaAUAYNMVwxwWATLpF5GwKg6Ihynsz2UvFcHaRKVUmuF4S4VS1PuFdQBPdIXRi/BzJABDKWjgAACAASURBVMAzOcChGA95yEMmy+dvTin+b08APpxjGI8KAP3xfO8JTh5AIiwHYxl/3xNdASCEvA8Aan+jKFKMGIUUC2iDTt4ULwqU3Ez8lOqX1XbfrgCQMCgAoEDM7XEmwkwcAEhq2QppU7zfhDEmfY4CBQAWZgSAaLwsTgDnNw1H4JJMUkqhHRaAk+mIFskp42ZtCKFSaCUBwqE5in0fAFSfJ0JG+DjD3/M933MhAHhm338cJ55vktcXbaVAnQZVq1IrctM3YVkKxl4FBwOzMgHjJcYCAIAokGgJCnBcpRBVcJIII/jJBM9ZgGipUKBkgmstULYrVgBU4asASEVlpUCphffWFtREiJIgsjQsQM7v31f4KwAjZOnLk5/85GkHFh/D4QOxsgDZx2FNACCvMK0WYGmn1sgPGCmH9E0pOIqJDppfPsCoHHpEObulyd8XCye4TpTJ/tZv/dZJEJzYUE+GO0wUKBy8cs6c8iaaQQCUQsQCjEKBtFVNhNViuM73q5nOuKLt8iJoFIcTrJ2UImtfcoqVyVsYXcMRxtO7Zl4DQ/U9KhcPAJ7ylKdMAMhJ13ljS8ZTx2FNJA5jAQCgh0FHNKTW/fRIU/qf/IzfAYAydRbW/NTapOqgr43/YgsA2tALrEVDpOkBIGHQKmxbkZ0Fz73+FslAObyE2yTb45pjUUaOk8XJpvilKNAcR3W/cdGiOK7nO18T+JLk0i8g4APYEeZvDrB8QU5V27rosVoBXhXOAIM2l5gDfMGGuhusbsB3fd4PECd4RIE6ANKHbglroKFaJdcBAArUARAA1w34W9d/nzkbXXsiibCqnfHThz70oRMA0BOTfZQ8QKUBGaBnmGzHkDt2xCkPfo8cq2iuJMJSCoHCyOJWi5FrK4XA/fkcNqDbUJ9EGH5L8Di6fJxoSz4AkHGacwThYUohqgWooI7GVQekT8KtOb2tClgdQwAANMZSM8E5HrELT52LDoYa2sy4zVN8APkQ4AfOWgFQLcDbLQBoygc/+MGThlapyNwmQnFYClQBZjFMOseTphFe7G84z4LVRa0A6ImwLjiVRqQGyIG3stscPD+eqdhLtWcFAICwEuYhJyQnU7xVm2W8c6XH2hHZSbSp7rnuXFpb+iKHAQBClLUcugpi/3+f91iD0f4GgE9omg8gCmSvRqJSldKsRd62ztOW607cAuCbD3zgA6daIKUQSYSFC+7LA6sP0DV8THAHVl24PC8ASB6ABcie4B427ItGgCR3aDY/eaE0wZeEyytRfYeXS4iZB8eN26lGQOd+RkJWtW/dDdfpXQRyJMSVsxPObFgnnMLHLBiA9Xvr330eq1XJeNKHVIMCP8sk9Ovc1r5HebRjb4sgH/aaEwcAzRQLUAFw2GK4qg3rpBMMXDxVmX2LYeW07utOcN8UXye4AyAWhfOd7GsV6vgpBApQHFmIpimDyEaVJQDUEy4i5N0KhHakL/pB6Iy77gLLPFfunoNrZbGBOKUQawAI3erA64rI38bAAqgF8gwWQBSsWtdqWd8uKZBJp/k4wQ6iRYFYgMPmAbKIdSFMogVFf+QC7Lhyxk3d4N6F398dAHU/QOemIxNdLVEHSACQa1CTHFVi7P3Iwi5AuT9C3v2eaN5o9ZRl0LR8H9WwiTLF0tY50BeWiROsmtWarG2I0cclANS+ZE0AgBMsE84CsDKZy9EcH1ar73PfiVqA8M1v//Zvn8KgAcBhneBqgutipLaFpeEAirVzuGrhVQdBLYVwrTBdB02naVsnugosYeNo+s1KpE5/yQJUrl9zEqN7AhaaFq3hh8i31IrbTulYC0dVAoBzQmsYdMkx3QKAXMPiAYAgAwB4DVMSYdWCdEBsnePDXnciAIi2CACc2x8A1DDoPk5wNeEx+/mMA8zHwGVlW/O61GjazmNDgcTo+QBCphI19Z1X2j7MSQ11YQgDJxkF0AdRJke29KNK+mJ2QRv5MHWOXf+0pz1tyjdw6L0mVag1CqDvCyacyQTHCa4WwPNGCbGuRGq/e5SIVRYFUi3Lz6BgUg1aLVilQYcV6n3uu0gAQDOjQMoUmNvDWIAKgLoQ/g8AIjK4rPdXAYCcw0iAcy/+nmNRLAwKBAA1Zj5Kou0z2agJqiEXQOgd3Ou1o7UcuieXAu4tz8m9ftsSaZ8vLSsnYUNQzbpGCUQp5dxOAE0mWDtzsfmugLrw934bu9C0DUcUAAWT/QABQAXZ25UPUDU0c/ugBz1oCoPKBOdYlH2d4CUAJBEGAA7HBQDCVilMX8D4ALEANFRe+jZa3C0C2a+hBQEfDbDAHEH+SXWYaw3NlmfUaE4FgJCmkKsdZwBQj0ePpY0lyfu7OMF8J/OWatDupPY+jaxABVeuBwCnYRg7AJjfCoCRM7xl/Ee95sQsQCYbAL7lW75loigAEAuwlfvVBe9aJs/AsbXvFGoAcC6QZNgoxJZ76sFYfADFWv2th4ed7DyDEOiXnWPAEEeQI5yfHttfe2adD8/J/c44ZWnkIVTd1kOxImwdAM7t5Dijjt0J3lcjd2BUACjTFmVLuXj1Ad4uKVCPONgTjKJkR9ioHHpu4TsAOv/3LKFWDuBTn/rUicbQgGriR+Y8QpA3xbMAAYA9BKOIz5pQjrRktmji5bQgmpaKyJxcXccyGufouZVrZyw+Q39kg5V0E+aUQnT+r816crMokPLxMwEA4V8+wKtf/eppTSilbNRfyjfsO9/7XH8iFqDSjWyKDwDmdoStDSK8cY4KiQTRZom01DNxRlakUyAc9TgBYDxAgPo9/elPP3VALC1Ya6Gqsuj97Nq+zlHuYwEIed4VAPTyAKOiswDOtckEi9Bs3RI5sgpd8+dvY5ct5wMEAMkEJ7yb8RyH0lmTn1PPOoktkVVICWaiQJxgBWujYrh0cCnSUK8JILKoeVtKjkavFGskSACgPkk9D17uNakAcNTIT10IfWIBaEFWCg92bEktVajj6BQv/kEdd+XbEaRqFUbClHtyXT26vGaC9WWuTn+OEtX1qv83doLP+gECCsTSZn67A7wv5doq8P26E7MAmQwW4OEPf/h0OgLHtEeBRgOppn1uoAkVZlFNOLBZQBowE9wjORE4USDa2YkNQqc2rPtd3+J+2Emu/B7/tXOM0KFljm0Z0QD31PBnjj4H1ERnjDXFasah8lS4E6D4GP75voO4KgP3sQC2c/IBAKBSoA6ANcFcAwCKCQjxARIC7j7g2nOOuhYnbgEyMRbeqc1CjmpBKgWaE/6qCSOwmbBKhSIwPmPK1bgTBo5wzgWqWrJqT4kw2yiZaNezAEKo/fVFR5l4/aIARKn0lfObN7j3Ba8OrWfaRCOqI17PfyDs/gGoNoHdrjIl2KyKaA4KCBAsWZTAKJRba4FEaKoT3I8tWRPMKKs+TxQSH0Am2G8AsP7ZL+H6apnWnnOUdaj3nqgFMDkm23Y9ryOVpKkWoHPaEZ/0WV3ECL3PEgFJdeOjH/3oyQmUdcxR3JnY7gxy/l7ykpdMFEgI8DijQBlXjj4PoDst6+Ov16MNSjtEdzi4yhtEeER3WAXHDhoT51LiC1goAFZMtC0vyUuZRp3bhEFZAMJpTeRC4k/sw823AEA4FABs1qnJyUsEAEy2k4tVRJrk7gN0Xh9hqfw3E1WLxLKwfmcPriwzQaHRaMaaB+jlADSfV6TmRdnZE1w101G1DvDT1LEAOa6lRqe6Ux+BMm9AQHGYP9sclTiIIAGAM3d8b7ysl+uAwH4Eu86SB+gOZ5RSji5/1ateNeVm8PPjBgDqUy2AKFDW5BLhA4Rv2q9K2AKA+oaY7vxmgcTp8VNcPZqzlgKbSNpQeYF7UgqBZ4tq0DY9ExogEUwWgIZ1RLr6GdsVWY/j+IkQp0gvPoAkVY5OrJQuoO/aFK3Tv0c96lGTA21MMrfAYd8D4KNVBIuCEWlDhwBA1SltOyqGy6FVjixhAZIIOywAuvPu7zjBfIBqATLuSwwATHYHQK0G7Xzf3zQmJw1Hl7I3mbh9thtKfBEWNMdR4Pi+xbcpHp2xoPhmtF+lP9rHoRWBSRwBJq3JRPddZIcFA0Eybr8VnRECwioTXKNAtewiwh+LoO+EnYV65CMfeepUOT4B7S6nor+E3PjthgsAWAQUKP6MtqqDbT6BEgD4DnGCjxsALJQkICtjL4RiyFGB4Shyddi5X7vvRH0AnSEIjgehofgAKFBelN3pRoTAAqEoOK03n9DWtlNa9PBX2ls41REjNpkw/xaSgKFCru8h0UyOhUYjbFcEAM4vLn3cAPA8B4Jl723elp5McN1+OOLSLKB5E0YWPSLQQCGcrOIVcBPx4cwruzAXfALWsTrclWrl3E4AQFPqhphaQbuFDi5FgTjyKJDzgVglvkmNAu3ja6wJ9tbvF98SudbImqc+4rMm21vMcVRJIAComeDRM7XDCtAc3/Vd3zUtkmI1ySqaWwSHAwsktB1qxSkUbVJs5jp0Y1QMFoujDbRJvwiNBbIjbMuir81TLIDrgOy8886bqNyd7nSnKeMaBVAtQGhDFYpkq+2nMEYUjQVQto0ScYopBBaBxXQSm+88A8jmyrnrqW3oCQCwpn7mwqBb8gB1XpIIAwBrUwFQNX51hNfm9Ti+nwVAj8DUh406Wa+v4cWqZeMDiM4Ig8oE0s6j06E7FUJT8FPmHxBMoE3nrMI1r3nNaS8rjkx4hTEBRnYTuGh0QpF+jXIBfAyJMFGW8ObjSoTFj/EbzXrGM54xZYLveMc7rgKgUiB9ZOke9rCHTU4wrk+binoZN21qDlgEiibh0npAby86S7iVE80CqNjsAKjCviagc3ITHwAFAgAWVj/zkvCzqhhuLpRVtdGIrvTvuzn0t8XixFlICyji4MyauUK1AEH0xOIADx5NQzH5NCphkL0VEyfw+G7a80yLRpPNZTVdk/cE01AcZwC7znWuMzmXa5ZuTRMF+H4LYdoXSzidCsfhXrIAFQCsHcUBAPrnHz9IkowCwOP9vsMd7jDF/3sOo4Zd02ftVwugZj8+gGtCqdYEv7Y3mo8RAGyJTRi0KqWjzvfaepymzOdelH2cFqA6dEz0Yx7zmMmZYwECgO6YdgtQAYDf084ogDchOmdfSJCW91OpRBw+7c8dPqV/hEufpOrRJaACgKO+vCIaNjF9GlvG2XhoQPuCgWwUn6+hX9ezfKiezS58GhaQn8I6Kv5De/gGd77znU+Vl8TvicLqghwAmEfAtGurZoLnstRz1HDJAsQJjgXgA9Q8wFrp9T6CvfXaI1OguQGb6O4D6BQAJAokQiPpggKNqhTr/RYZP2U9nMAmqoOqOG2NJhRRAIAIHIqBMuVkBs+YO33BPZxJwsUJxpk5joSzv1Zo68QGwASfIGc+8h4vFEW0BsCqlh1ZTZ8poeCjKCGh6YVP9Y+mNzf8Is8ADPOR0gkWMTmAuWpY/SOUFQDVBxhRoDkAVMXVfQBOcCiQPp7VFGhuIHXgVci7YHQApD0AEAURpUiEpgOga39ClEUGAFSIgNL6BAJlQYdQqdAsDiBnk5BwtjmIvu+a0N+EkQPNAWYFAFMegHatGnSL8FfQ9tr+gLNmr6P5M19zCkXkS7KKEjCHfoAzGtQYCDurZczO+xcy5h9JAmaOE9qsfppnxgKgQI6SzGtS+4b9OTDUuRmNwRomChQnGADOynLoJfozJwT1ns7hKgWyULSAWDhnlROccyvrffUe/48FEAUiBCI74uicPgufw7VcS/uJgXsRB5AphQCC5Bu6VmctLI48AwAIz4oyqa1xbRy1JZ5bBSqCnzEE0LVWyWfxS0bKomtY88Z/IvwVLPW52st7AIRLjUdmOImwuShYfAAWgHLZWgw34upLFKiGQSkwVrvS0krPTsoPOFIYdA71awAQbcC1aWUA4LR2HyDaMhpaYRetZpMLc8+B8pIFYU7Upk4kAODZtkISAHU9aE3q4tEOOQPCktIJbaJTMq18ANWgfAzAijPpt7YBJlpYP7UBXIAc4QRYuQW/a02P+2lz19HWKAx+r01CHsHXJq2dgjngEdkSPtWmn1AaPoR+1jdSUjIoE+tI2JIJ9tyadQ1I8/oiFiB5AN+diTAoP0giDF07K4vhjmoBAoxuZrVrkTlxwo0iIFssgAW3MEKIBJtgEXymnS9A8KqpJiS0n/cREwqUhjBHEFEb92qD8HCAtWtPLCeQI6mIjKOt3CCvWCU4QCj0Soij2QFKW0Aj4eSHmZeI4ofQ3BFYANB/NIVmxuVFtbQrFxEAEGg0RKSMr6DvrsubX3IdAWVJXadNc87PYCkl3QBAVluYNDvPehhY2+gVxUQ4rYk8QwfAYemPvtZSCGsJAMrhKa7I21lpAbaauRFoOgBMBM0plIlqoCUVAJ1eRTu5h5PKPBM8n9MctBoNn0wqLQkshFi4kECjSATU4rvOPwJDKzqWHEC0TfvbqcUXcC0QAAoqZKG0rR+u43fkaJOUNRMwrz0FNP2z8QXN44voU+gOTU/QWRmZYFs2hYTNhxBmolZALdOttEObngOkLCdhrZaC8ItaASrh9gxJQGDRnmibfcHoYLZG1rUJAGykF2nKqdpHKYXoa1kBQCnwsSivUfhb3y5SCrTm7I2EvX824vMBgNOhCREtLAqUuP0W/yIRlbqA7kudvQUkUDQqq4A2iKCEcqBdQMP6EAY/NDSthDcTMoLPavhNqDiS2vdPKM8zaHLay8J6joyre7RpLvBdYUlAcU3KEIBYLsCYAQAYCQQKEgrkN8ukr0Ca06OzmUYb8SE8S/9cK9pDoMwRa2keJPdYRMLmRRzyJa7Tn4RZ/fZ8APAMtVNHKYcereOoGO5iAYCtdGgLAEKBZHNpPJorPsBSDLg7k5lgnxNsk0vriWQIZcoAc2BlGwkSgRM6pcFRAv4DwYtgpV/KCmRpZY4TY4+g4OmelTN8ajFZeHW+i/+SXVnpr3v0BdVAU5IJ1kcgzHii3T27li8YpzFUn8K1iQbV5F/2RKNrfAHUBjhFzlgV1jNzp1+sCovJ1zqOatA5C5BiOBYg9Vld459VFmCO2ixZgZH5SmTEAiqG85IIGhMA8oKIOvAaGQnX7s+MoFlsVIf2Zlk4xUJs+Dvh4OBaYPFz2tohWfh1nNY8SzJJsR0+DwA4dV4pROhcN3e4Vo31V0GuYHWNzLWNJwAggccS1VMhtljfJPo6d673+g6o0CrWjUVkaYA7+wOAK1YgpRAibHMvydsimEtRINbTkY0UFeWE4p2VxXB10UYLstUv6AuSojBOsL23yQNwHHuh1ohCReDznfZy0GxqfywkwbWhAy0hLK7h6KIO6AAB948/kEXVNsvh1UJxaLfuCdYPAOnFbCOfRv9EmvQJL3d2ac82V/B3IQ+4qqD19cj9mS/ULVskPcu4sm8YEFOoxr8wR3MvyTsuAJgDIDT+RIFGVmBNGRzH94vl0HNoXgNA/z4Uxm8WwLF9AICO0DaiHFsBkD75TYgsYO5NZSiNClQJYbo2yTTCQOtkP20FAArEOglP0lCxAGsOWbRoB20WqH4uAoRmoEeqTedeDlJpX13oKtwBQwdevSbW0/g9M1bMvYIFfAXf8Uk47tkPMHpP8HEAQK6BJQYAPklNhGWe1ub7OAT/1NosHYtyVADU+w8W9CAKJNryghc8f3IwOcGxAOG+u51r8XufXOq0koosKE3OYWPmE6/3/zilqIrJjYkNZ4+2NskcWVpfyNL/RYOAAHWSO+Bc9pDhaPIrwNcWpwpiBf3a4ldLUJVABfDompE10UdgIIgiVZx1fgi6xE+45z3veSoMulSk1mnqCPD5LJlgAEBHYwGyPmdVNehhKNCcYFzgAL51R7D/93/fPDmaADAqhThYxPxzUsABAHycBSaseCQ+TZOLJtRjDJcKuEIL/OY4K6yjBWlDgEKlmGZJNhZglKAb0Y+uLDr4A26Cl0RWEnER4hGV6TRy9Hfu632Ys8TaIJA22Bg/v8l8Gr+8hDf45CjJmjTrlkj7PSp3gRI7XSICAD6A0HBKWWo1aAXQSVmBE9kRZmAHTjDNgwKdu3vRi164u8lNbnzapvgLBg0Ak653WMZpAGBBRDTE+UU3gMhkiupEoOYWIdajLg1Koj1JI21y1FQpclA5jF0Ddm0/Et6qofP/CAqAoUDVcs1tVOmUYwSqNYtTwVHvTySJJY1fIjIHnA4vTplC7u+Cnr75vFvJkfBWAACbNVtygvu4zhQgTgQABD9RIBrw3HPPmyzAjW70wZO5HeUBzjnngAYFAG95y0GSi9birInZM9cOvlW7kwzsmkCMvtc3gu/ENg6qGLg6I5ngSitG2nAJAL32x7PlECTTRK3sXhPnjxM81/7IIlcfYYk+hab0vlSQEk50iGWmCO53v/tNUbQa8aoAqGOOH9LpTxfYONooEAuQDU2VAh1WyA9736QoT+ZoxAvoCw0uFmzjyQ1ucEEx3IW5NouROP/5u9e//j8nTU3w8XbJHKFKmqqXQuwLAs8BLDkEFaGytHlBRmp/CEDdWO4Zoyxmf3Yc5HyOagkAsAJKFHI8ukU8KgA6Rel0qVqv6iinGE54Fj+XCZalZ6VYCFSRssnbbDoAusUdOcsBgBwIsAG/7PUoCrSvQO97/WnzdJIACAV61rN+aPe85z13d8MbHhTDXbgcmvY//4AETS+8UD/z+kl7Eh40QhKFlgKEuZ1eW4HgGdkRxgoAQN4RxkGmFZVgcI7RogButIlnzsJkLEqU8WAOp/cEywMkHHucAOgaOc+PD1SpEZCiJYTTeIVBWUFRNUEBvpaIlZIKvhaLtVbCMGcBPENSkvCzArUYbpQMXfNrlujulvU/kgXonZt7YBzYAOCZz/yB3fOf/7xTAKjl0HGs4gjTQoTfs97whjdOC8Q0S/3PnduzZdI6reALcAYJJ6HMa1Itlk0yQIAS0YySaP4vlr4FfBmTfhEmGVda1QkW2qpbIpe471F8gOr/VPrk8w4AmWB5FCDVX0pBf9U7oZvmXujaOtQixE7FKggqBYoFkJGuVbxzDnenWUuWbgT8JSBcJADIfoDrXe+6Ux6gvr/qYKEOtP8b3/iGKS795je/ZXeVq1x1shShCkunNsffGPHzEUVJREjdjL6hJbEAhAAIfId6cbQJrXIKNUW1nCLaKAtWBSBUSKwdAFCLNQB0LXpUANSx11IO/8fLo51ZZdqe8lHLBPz6LZNM8NFO3ysY7HNcQTACAAXD6UaBRNvqbril8c7RnH0/v5CCOQoFWgr99QdN/uzbqkGf97zn7370R39kd93rXue0PcEXaOXzp4pJgmdjy0Fm9yMmjZ+isjnTF0FL30Y7uroGpJ3QKuXLACBBl3eEac93Fh8dUC6hTeUUrEHKOKqT2AFQuTc/RpGaBB4fBqXKxvuuAbcAYGSF631zAtIBgALxAQj6ve9974nuaVvQwlqgnxSAshLA9708yaj9kSb3vGyJZAFQIBYgFrTvUagWa+RTdGuzZDnPiAUYTfwSJToQgoMEzLOf/SO75z7XjrDrTQDIhhgdJYy04ytf+YrpoNpXvOKVu1vd6gumWvtrXetgj+4S76sA8Ewapi9Iz9z62zPFxAGAqQ8AQhEOqNh/TEDgL+DEBAB9CYCyMafz4xpx0YZ4u3nAp2t58r4+QOX11fRvAUBdK+NHLVWDyol4tZRK3UoTU2/FIhin8WcLKgXhmYA8iutnDo2bBaDYCD8rMLq+K6glAMzJwlbH+FAU6DCm+PzzD8Kab3nLm3fPetYPT04wCiQTnDcYEgqCaIJe/OIXTRpZeNMWvY/8yI/aXfnK77paJ57Jqxq5C1YcwWjqVJOq1LRAQpMAkJPhMt5QK5EsbQKj/4sgyaaq60EL0KJqqaogaSNlz3GiA5g1ANR2qvDX9ajC0oXA3xWMtT0AQM1w/nvd614TAKpTmgx65jXlF3wDGt2P+crOs7rtND4QCyAMaq4Iv3+Zg1iC2r/K/ffV+CcOgIra+vDTwULDv3n3nOc8dwqDhgKhEa4j/CbngIv+3mRqZWRvfOODys05J+nCdCs5hIMz5/tkRJAzwaE5Fp8FUAskRNlfkZSK0DxPfwi/BNojHvGIyUGk2fwmCD2JFgHsCmRfAHThHwFgJPyVVlRaZvyoWYSTUkLvqqVMe3VMwI8aKW5URSopidfHN6raGegBgIJJLVAo0Ij6BXC+u3CI/GAF0qd9gHIhqnQYH2BOi3TTdfrDpsKeyaGVyIoPkDBoDqhVtvvSl/7i7rKXvczuZjf7lEkTXeEKB8f6HddPLEDVgMw48682xgLasldfkxrhrZPufv3Gn42J5RIiJAjKM7SD3uVeY8D9gQalsmdBCDQ0bSvA6zzM0c4l7d+pUygQAHBQEwVaopqZQ0EC209Za5WkSimsGSWg6jQ/nhEKFAvAD0CbRnJTlUXmJX5LlFpdix5CPREL0DVZ1SoXduCm6dydf/5bpiNRTPa1r/1+pzbEEKQcgf7a175md6UrvfPu+te/we7qV7/Gccn91E43sfmbYPIBWCYLZ8NGiuHcZ/KrJqpjBx6L734gkDMg/DRcSjRyPy1IWMTY5THQphyMtWbmjzIR3fp0HyB5AI4uvwyAQ09y7ciCAbIiQlqdAy1IgAIqJ1FRGyoYAHQKJKoWMKWYMetUaay+5Hj3kUWoymNk9efm7kg+wGEBYEO8iMM1r/m+U9IFBTJYWdcM+vKXv9zuild0IsPljrLuF7q3grSCwbOF+yyQ/QB8AMKZia1CEM0YgYi5ptkBQDu+u/nNbz5VvEbL+YygeAZnEr0TUk0o9UwAoNPRbr0jfPEBWEHlKUKdCVF2AEQTm5vQSb4ADW9TkkiRXAEA5NVM6KPvKwCSCNMGBSTAUM898vwcKy9YYF1YmCTi0q8OiBMBwGgig9yk0A3+IFn0DqcK2wwWADhcV7vaVaeXRWtLVIHDa8DyAO49eA/WFWYBEGE2udGwc3yxFCYPcQAAGtJJREFUNpJFy0S5HwBoMAuE+iiFAIAqlP6fjS9VsAIAzzB2QNCeLHUO4+Lf6C+ujS7Rmgrucjr0XFZ5C8Xp4My8jAQhfLmun/4r0RAFspFeFAgAAv7MaVceoaXVpxLlEja1fjYkucdc+AzolZskD8AJZgHcz/oLQtgpaAcbahgKxaLyN0TnhJ8FKbKf2xhHR7eccQpUJ6NySh2lAWhBERFZVQ5h5YLCm05tg3oxd0KPDsg+EpjUzBsYAEXjVK7ouxypQeiE6Xw/0lp1z+yBH3JwyFS0n98oGPPvxRJOaogTHA1UJ9T/a5v6pz3/4jh6Tk6C0DeLS+gJgnyCeVIKIekG6AQmh1pVReK6Ou5En0It9MU1eXZAqo0c6hUBzp7ijClr4h7aF/itmzyARFcde8ZvfuuLNiLgB4rrIPiQdUiRH9Abv4JDQAMSCgYAYh1DpdR6KXfhH7HCZMh9+iVZp0xF/oSflXOQLjILUBcmWsDgaJFKJYAgtME9tMDjH//46ZwbA4TobFSvoTQLCyR4s/9H02pDVti1nEx/e66sMU1SN42bHAk0EwpMrsW/LXje1eUzC4AGoADMt/P2WSTP5ujVH+1oM2du6ptrLC4gRVgIiv5ZKFWmfARFcCpBKQU7okScXAf4fA7PdL/+UCRxmPN8Qu25xh4B0B4hAa6sCfB5BjBHW5pLFINGze4w7dK2QKocWhBCGJT21SbtHWvh2Sw1ze4en7NsBNy8R6F4NlqbQ8tofEqP72P82nAiRixA2tenvEjcejk9WxJUH1BLESRjtbGfA92PvK+AvkgsAEEwQGW1UKyDtJyISuLChNhEOLhJRhT/NUj/TCzNIwRnkrRnEYDJwKPBtCFEqZ4cuLTte7U89gjElzCxNAyzyanTPgEVhQBCbQcs2gQMQHIOkHJozxfiNPmZUIuLh7JY4e/4ryI31kMbATuhpqlkTX2uf0BAkwGmLDAh1SaBE0LMW14IlGcLzepTBDsHZtGCOdnBs5VqcGSTYwAO2pIzam79UBDWhaNqHhJiBGb/9EtbInM0PdDmHCbPJ/TWR5QnB41RJGqFhENjMQAasAm4Odd/go1ioZnmRG7HHFqf+iPzjx2QHQAwR57NfxCiNofW3Btxsl+j+mT9/2sO5KGd4BEFytEk55577sT3LDpao2afpjep2YlkWyRHmJaj+VABWs3gACCHQfneBNOE0YwmGgAsLl5IgGhgk8xUhg4RatqaAArLEVya1UITLounrYQhLbbnWGBbIt1vwpUIe7a/o4FVo4a+sCRpExC1aZy0OSH0fAKp7ZzuBoQEypjzEg9ABQT9oVmNBS3TvjHmxd/myPNZF33Khh7c2Q/hJljmxlwSQv03PkChkZPMcx0roS+E0z8AsF6AYg3jN6A0olvalbyM0gDqnH8U+mOus0/DXADyk570pOlUPdbeEe7AHv4eBaMteQXt101J+qEokf/EsrAgLLX7PbOGQc+IExwzFUSNAGASaHeTSIP7bfEUfVkwCx26QWAMiNNDYxM6E8MnCF0xkNThRKgtHAHTloUjBNkcT9P4Z8LDowmT9mhLCxi6lO2PmbzskdV/CyMMahFYNNq4mlftWODUAekT8Bu/voQPE3og8Pyk/LWFhgCf8ekXkLIWddzGAExojfYscNrVpr6llNgcuTYlCblemxl3HHQgCE30fG0QfuBkwdBXFAhwrEsoXZxNfUWp8mxj116OfwxYfJ8yd+MluGgQxYbbW+tE/7QdAQYAR9OYC1o+1ouCs1eDFaD8ACAn4RnbGQNAFfzR//MZbUBT6iABIci0Da1ssN5aYvAQG1PJbDKzgEJYaFT/DDBn55uc/lz3xyfIwpoAC5nDqarPkUXpn9W/CQ/tJA/g+QCQszbr/fX/VRnU/0ebEWKAIMSJZLiO1gVcApL3A9D4/A3tW/wk0KpwZB5ijeZ4bo1c9T5mPhNuNm/6yYqgKGipKNDcdsWMP3y/C1/66Lex86vy+llrb15ZbgrS3zXWry0+GAoUH4C29yOAAKAUptwKpYpmjTLFx2oBloQ+WjbOEO2J2uDGhAefRDUMllkV8kvSx70mHrIBAFCYcFqLiXetMGSc3AwqUQ6aiVMHDISeZqons2Vh6kJHMGrYznXaoO3QEwDOmaAJg8baRXjqBNc2E63KvLBGEmRi/yxOnks7Ahkl4bd+c6D5JcBCCeDJUQKpaK1OZg1B9ud2bZj+VMDnnoDJ8723gUJ6wAMeMCmt/m6AWMsKotpmlQfrk9ofVoXFlhfgwBLuKrhVxtA+x+awcvEBtEtZAijqyEcTpAi1q0oi/Tk2J7h2rk901S4csHj6dhPRbngbobKonMp47rXwSfuEj5kUgeAEuR7ycWdt1aPMM0C/EyIMh6+C2bX+KQ7ztmxwBzZtBYgiDTHTAFDj81X71fZ62+ZJ33BoVpAWxJ1RNmDzN2pF0AkaH4ivowwDVzYe/Nn43VfroEYL2+lpv6b/3a/XX30CAJGg+9///pOgjqxpXfNuGX2nLXOJ4tH8aC7LzMH3L5Gzuo5Rhu6LEnWPHBGfiKITOmYByALnmr/k/93aVUU5t0b181UnuAOgCkE0I7RzFm32prGVLtPIOi7+S6swV2K/eFs9vSFaI+W2gGSwfptM5k7kwf3arhsoMpCRyT9tkK0gLv2uixkAiDixWHiqyQ8AqhBVM5829DWZUf8XcVHyAVSARPvRfKweYcNnKQgAkDF2L7/IfFEaTL4xoyL4eDYDdUpYtbs2oqW3LH7tOwokeqdfNsWLMnUAjJRILGzmhCygwtZcjZCxO2LFGPLGncxlzyRbczKEDXh2igr5VzlMzIFd5IHlrBWnVRbOGAWKCY/ZrGjHnXFoyLTYtBZN7jPIpeVZAODIDrB0NJOXsmSDRZ+ENE0mEHCSUStmLxtIKhhNZs8IVn45EuAIT8bBAgEABxdYA4C5IrVYRP3Q95wjyiFkynFZFE8YWNofDXCP8QlHRjGIiCREyxll7jmDKIQomnwB8GQMntczx/W7LdnwrtiyH0AiigWoAJizIBl3BNm4KxOgoYXBrVte7F0FNf5HKLR7WU3g9x0ZSq2Q38DEinLskwMZKcEzDoAITkKazDxtJwqC16I7hAenJ8RAQMOaCE6Q+G09DiOLEWBlUwxeij+6n+AIe9GYwnAxf5XvRgPGvEYrL/FB1wQAnqMUm5nGMSXowr9HGjWcPEBIXzjUoh4AgMc7BZoGTCJO1ATfFwYGCi/ySEQj9IkFAQDKgrYLTUh2uW5M730LJ95ClyLEIwDUGH0sT7V+1eqx9tabIkRj9Jvwo3Gjs1+zRpnDJD21U/2TCDOBr4cnRFZi8aryOyMAqAPP/3WUlufk0dQ0AJpCa0E8QJiUvPiBMNDmtFmN39bJrWDIoa4iA6hBsoiEiaNMGxCEbv5qG2uTUQGAeqlRomHkAfR1KwAq+ACAwyYgwJe5613vOoE/2syc4dooB4dY6YHva0xcvxLOND5tit8TVOCXXzCPKTeown4YACQKBJiiQCzAGgBCJfWN9jYmypCgsvS4emjrnKYOq+g+Qf27U87KHMICqpVeW/ND+QC9Exm8AaA3NLz/owHZ5gfVCVfqlAW24KEKGWQWL5QlFibaCVe2+LgxnuyHYOVl2XkpdKcqoQJLFiDPSBQIALR361vferI4I5+jK4P+t7mgCSUEKQIWAG+thV+4diwAAIj6jKhW2qZcWEOBBhbE2PFhfczmmyzslnH3OQYAYw8A+CUjANT7rFc4f7LWaIswJ83PcnXBrILdrcqIpo58nn5dF/gzCoA6Ad30xpxt4aCnofDgFNxTMeF8VwWLUOGGfAMWQdRIpICDJWQq7JpXJVUnK/+f8wFCLSoAaC0AQLW2ACBzkjEAPRogo6nfKKEISAr7EtPGt/FaG1AAui52VwrmIqdTGD8rwkkmaCwioMUp3Gf+owC6BdDfOMHVv8gYCT9QivbwZ0SvCL89EMBeoz3R0t1KVT9kRDG7HHTw1O9720tK70gWoHK32oHK2/rAqkn2HQEZUYvqZMfCJFmS56IFanhEnfB1sXYah7ntFYLVP+gmNe2HS+akaFoQAFCgWIDuXNdxpxQbUPQ/tUXi/igQZ1jcGh9OuTe6wELIEaAKHOREeeq460KFEhkvR5H1UCbhPiUDNHZqg+boRBeKasU7ALTX6WXWJ7SRwy5oAMgiZypo6zuJK6UbycSckNZrwwoqxRyNrwPo2AEw0vZLCM13o45EI6y1mQWqA46TyK8gCGLnnGWxdLxV3oD2SaRoLoxZJ9n/aWpOMADQZN4tDAB5TdFIQ9X+Vcvoc9qR34Lq0JKcd0418NOWIk4AS/hp8nqidQVn1b6VrvEFUCJtC5USvJwwN9KUc5GsWO0AQNyeD8AChALVPlThp4TU9whvCm6IAAJ5p2BdBrYK55JVWPtu6zNW8wBzC1/N/hL6tnakC2Tn1V2D5ygStIBAccQJF8cVN/ab013r5rspT7/DZQkl55VWRVtEtGqSbQT4Og+9z3wXwQHtKnUQ4cg4UJacslZfkrG0sLV9FosGZhEAPq9SRY3UBRHEhBErJ66UMJSrlkIoNZAHmKNAeVGghCV/QT9YX1Y4cf45qtJpypoQn8T3hwJA1XajTu470G4e58CQia3fZ0FEcAgafk0Y8HcaFreOgM05mdrTjjZkQ2MBUprcOfWIu1bhzJwkryGkSVPL9mpLngH3z/a+0MGleZubo1BPzyT4rBgfQfsAzDcy/qqVu5OoDRbA2AGg5gH6XBuDBJdnSFCxuige4Y/VnQNAlZWtivFMg+BIAJizAkcFQB10F6xOCVzLL0CJcGq0iNalfWnyvBBPoik7yEZcGGUhPCxAd4K3AGA0F5Vj583xns0Z9q9q49DCDtKR1RpZR88Xds67hGlmFI5wUgR5NWqnJ+ljKFAsAB8gYdvMMRALdXLwfYd6qfIVjs3e39Hany3CPlTW+xyLkomP6TwJAIwoRgdBeCkhJvj4cWrb9RklslCsQgSvasFqAXoYdCkP0Cd0pKWrsKZMu1OSzKff1dmrYJizANUPIfQCBIBMS3PEhaT5BwSalh69PUe/UgzHoUWBXE+o43zLTgvBoj7CxHwa/7Ljrdf1b7ECZ1q7b2l/aAHqZFf0jkz/0kO2In/L8+pCj6xAnLlscEc7+AYSMxI1ispoQ76BBWSu4yAnE4wCKYZDodQCcVpHRyuuTWy3Wl1jR+B93q1LnbMlx7X6I5UG8YOM11hYA7kTmXdOPUpXnfr0o1IgTnAokGuzNZPmT2Gb0gwKRdGgPnYl0SnWVjlYm9cz8f2xAuCwA90CrCXtWq1EdexoRHRIgZXfKJGYefYc5Jx/bYsCERrhyQAgtUBLYdC1RQlw9SsbWqrQR1i6EuhCtGRtajY17Rg7vo4Seh4rmOPks8mFhifkAQD6R8jvc5/7nCrQk31Xs2QOtSPO78QI/kvO6cn8V0q3Lw1em8cz9f3FBgBLfsGccBAGQmcRWQOLiMdyEJlv1CBhuwBAbkE8XS0Qq7FkAarQdoDOWc6aL9Hv0TErc8I/arNaxk5Jfcci+EmewjglEwm+UhKC7LrU2wvbAoD9upxqwi/ULCcgN0L4a6hT20vZ3kqFzpQQH6XdvZ3gOuHVJ0gn1jTXqLNbLMC+94USJWMpPIgfSx7hyMoJOIccudT8pBguAPC5xc0Ca7PTryqUoyKukVD2dqoVqN/tY1E7GDtYAgZ+gdg9igjgojjGaW4k1/gOtkSKHonzC3WijPYHoD3Z273k7PZ+7zOOowjzYe49EgBGDzyTAKjCtzZYC54sbYSQ6WcNJKg4cznrXgwbP6YFUSARE1lNCar+Io4K+kpvPKMDYA60I7qTPtb2R0I2pyy6n5Fiw+or5PgWhwzYrCKMKVRK20uiEXgAQHM8m9V0jzL2hDpzJlA0+xIQ6vjPVhAcGQD7ctd9NXm/fisIYgGqxXJvSrhtrSMEyhJwfhyZmRfiU8QFAHlPcE/Dz4Gvz8XSdVXQe/tzlnVEA6uAd2tThTTzYfxoIAfZngPVuqJDrIAwKgDkuHr5AxaSlRBGJvy1TfM556iPhP9sBMHeAKiabsR7D2MBRgs3JzyjSRxpxQqASs/iF+QEO9ENwiBLyylGEXJGT335dmpS5hZxTjNnPmqkps5hd4gD2BEVGgGsAryPs85hnpN+yCDLngt7ygFwkAk4ish6KLeW4WUN0J66jVW7ae8SCYBubqMVRmZxjap0Dbb1+jVLUAWjW4HqHzitgVOoaE3IEEWSK6D9AWKNhtS5mLNW2ujFgp3qROBrewkxdsBUkMxZhe63ZIM7CxAak727rEDCo0o2UD9aX6Agoc5RhGersqv3bl3fk7ruUBZgTWMfxtTNadClifCcNU6cvvbr8jfB5CAni4wSySr7voY//T+RlIQz8/wuzFEEHYRVYKqGr1WwVZkQ4ghuKmgTtkx0p9KQGg71efofIAX4qF6yvPwAIdMAQH5EmJgFUGBYs+e1//us8dslALpg7ivAfQL3vb8K2ZLp75RtZDk8m4NM+8kkE4oc9JS269Ekyeh2cEXrXjC2t+68GirXXepS9j0c7H04eA3swf9PH/vB5xG2OLPZHRZA5AjE0JG0cwFV8waVS03te67/O3Xbe9oud7nL7i51qYMXjmQsiXYBhqgP/p9n1XF1i7hl3S4RAKjCUDViBcqITsyZ8C0msFuAOVB1zVi1bxUcnydy1GnLyNzXxe+CcHB9hPttr8iM6E9/5jMguCC8Wi3AwZs1TwfJyKcYa+MLnvm2/UaT8AcQeXfzBf04eBaQXPrSlzlte2Zvv8/FFmuw5Zota37c1xyaAo060rnpaOJy32hCtmiTDqiRY5hrKs2poFwS3IyhWoos+NIi1vtOv47UdQCc/vdYSVRrcfpsb5mnc865wPL0tergrvN1YEEudcp6zNG2fenQJQoANWLSrcEWc7hlgaumnNMK1aGsFiqmH42Q7cwR4JWzuwYN4AjnBIY8c2R5xkCk2TvFufDfc1byQPuHMl1w1Zb5AYCl6+rccIb5PZmLy13u8lNegLPsH0qUfMiIDo2E+2wV+Aspg32qQdfMT6oyu6CEcmzVGlsWeAsA0t9EYPI7VEfRmAiQ6lFhQf3LWZ18AsIvPi4qkv3G/Tye0ynLgdatPkDoRwC4Noenf78NABcWttOtzsjiZS6AXxTIoQOywwenZV9mejUVf0CpsxxJ6qbm9hVcXAT+xADQBaPTiDU6sUVQ1ia9armq3QMA0R/hT/UvyiBEQLLYnGGCAQAO+nIKg+cFANWPqHTppAEwz/8vTLsqEHqZsyiYZJfcx+te92+7P/zDP5oA4fgZu+NyElsFwKgGaMu6nU3XHKsPYFJT3OX/maxKg7ZQoK3acisAehIqAMiOLXXuiuBouTvd6U7TYrMAT3ziE6fwqO2BjuqmERMWrII+34/O9Ufc/8BZrjz8gr/m/YBlIaoW4MDJvsA/m2Z3yku85jWvnXaAKRK86U1vMiW9rnGN95jG/vKX/8ZUGoEGGrsCwhQGRvAvHPU6m0R7W1/OCADCkWuWs9KgfejLtmGMrwrwatgyz05kyDWObnQmvRogR5QAAF782Mc+dionVg7geHf0qJ9AVunehYV43tmtQn46ABoJql++7as1ini6P3Jwk8+EZAOEN73pf3Yve9nLd0996lMn+neb23zJVPB2pSu9y3SNDTL2UkgMqgKVGEyuYB9rfpT1O4l7jx0AVdtWzdg1f3ckM9g1rb7PpEQQaqKpRmvyveKwJz/5ydN+gdvd7nZT6t/COyrdzy1ucYvp+JL6crja3+rbbLVedRxbx7wm+CMrUulZDQfLdbB8j3vc4ybaw/I5zycnQXCK7aFQMOj1Usqm+wEDW635Pmt20tceKwAOtMz5wzF0ITlpAFTBjDVKtAoAvLSPA2i3EyBwCjnI4cB8gJxnOhL+KsRbBXVf0G9tdxSRuoACHVglAq7y1bhVwjq+kf+Tw7AkAlkGNVLKw+vLvKsfcFLW/EwB49gBsLRI3SKMrt2qDbdMSHeCu3bO9w6yVSNvkZ0KLeznYFpFcvqjXBo/rqdaV+pzEhZgq/D3MVYLUAMBTs9wqNUTnvCECeR3u9vdphP2UiKRY2dSJJhXuFb6838WoEnh1kXqUZM5YT4qGEYAGFGUnOPpCBWC4JQzGtDntgiiRD63gSTvNqiL3wGwBZxbrxnN6dw8z0ejDnyASv9Euez0AgAOriPaUSDhXpZRiDjvMlMblJMf/g8ACyu3VfuPuOqSQBwWCN0H8IzU3lcn2EZ4JzXbHHKXu9xlAoB7c4KzwrO73/3uk4DkVInQqO4QbhXsrdfVOV0CQ/oxoj8BfbUAIj2cXAAwPmehqgDNK6n4QM7+4Qc49U0upB7JPvLvto7pbLru2CnQVm0+t7AjYT8OAHTQJWmHC9sKyOF1jo73UgEA0++dBzaNOFUBMPyuZ+X0pNCZWNi5earWrfsSI2rSfQAUB81j4ZzsLMrjKBTWwNwQfPsFOL+iQznstiYCL5EUaE7DjKjFkoO0ptmOQ8N0IakaMDkA2yPFwp0qZ5HxYPkAGlIEBCVwkoQtgc7Y6VskLyoLkLHUCFenJ90xr/PhPmOU57A91C4xYzN2P6wCn8fxjahh1/6V9h1WQZ0JhbFvm3tbAJPYd0ctcfq5yTkbAEDL03TeOYATi/LkHbg58gP/JwDA0Q/aPQkhWLIAndf3/owiU1UJ+L98h4wvIKgFohjcZx6ER1mE+k63kdU7DAC2+IuHafdEANCP8pgDwNIATgIAlfb0hU/WGghowqod9ZuwA4TFnzv27yQowBoF6gu+1KdRWz4T/gUEdUH+r428ejb7gCvN6lbvMIJ6sQbAVguwFQAj+nScFKi237lwHOMqSF2zztW8HEcf1zTWmqLY4nMtCVsseq5ZWrM5wT9TAOi+zdpcHeb7Q1GgPlmHmYAucKPOH2e7VcOPBGLEl13n86Wir5OwAnP+1dYFnwPAaE5GtKn6ciPat+86bdH+dWz7tr91XqZx7VsOXanEcS3+3IQcdeBb6MOS5ht91/t0XHOwtmj7Cs0WBbOvdeljPezY1wDZgydHlYOlub3EAKD6A2vCNufTLJnkM7lI+1qAw4Cl+0Br4zkK/dsCgG511tbssN//f6LFaMNy2BGXAAAAAElFTkSuQmCC" width="184" height="200" /></p> <p>Gọi I là trung đi&ecirc;̉m của O v&agrave; O<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>'</mo></math>&nbsp;thì I là t&acirc;m đ&ocirc;́i xứng của lăng trụ.</p> <p>Giả sử mặt phẳng (P) đi qua I và chia kh&ocirc;́i lăng trụ thành hai ph&acirc;̀n (H) và (H<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>'</mo></math>).</p> <p>L&acirc;́y đi&ecirc;̉m M b&acirc;́t kì thu&ocirc;̣c (H) thì đi&ecirc;̉m M&prime; đ&ocirc;́i xứng với M cũng nằm trong hình lăng trụ, và do đó M&prime;&isin; (H<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>'</mo></math>) và ngược lại, m&ocirc;̣t đi&ecirc;̉m N&isin;(H<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>'</mo></math>), l&acirc;́y đ&ocirc;́i xứng qua&nbsp;I&nbsp;sẽ được&nbsp;N&prime;&isin;(H).</p> <p>Do đó hai hình (H) và (H<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>'</mo></math>) đ&ocirc;́i xứng nhau qua t&acirc;m&nbsp;I.</p> <p>Vì v&acirc;̣y th&ecirc;̉ tích (H) bằng th&ecirc;̉ tích (H<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>'</mo></math>).</p>
Hướng dẫn Giải Bài 1 (trang 99, SGK Toán 12, Hình học)
GV: GV colearn
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Hướng dẫn Giải Bài 1 (trang 99, SGK Toán 12, Hình học)
GV: GV colearn