Hướng dẫn giải Bài 75 (Trang 96 SGK Toán 9 Hình học, Tập 2)
<p>Cho đường tròn (O), bán kính OM. Vẽ đường tròn tâm <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>O</mi><mo>'</mo></msup></math>, đường kính OM. Một bán</p>
<p>kính OA của đường tròn (O) cắt đường tròn (<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>O</mi><mo>'</mo></msup></math>) ở B.</p>
<p>Giải.</p>
<p><img class="wscnph" src="https://static.colearn.vn:8413/v1.0/upload/library/17022022/z3188358274970_b47f82f3ce630f9334400b65eb8ac035-cmPg9Q.jpg" /></p>
<p>Đặt <math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mover><mrow><mi>M</mi><mi>O</mi><mi>B</mi></mrow><mo>^</mo></mover></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>α</mi></math> thì <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mrow><mi>M</mi><msup><mi>O</mi><mo>'</mo></msup><mi>B</mi></mrow><mo>^</mo></mover></math> =2<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi></math>(góc nội tiếp và góc ở tâm của đường tròn (<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>O</mi><mo>'</mo></msup></math>)</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>l</mi><mover><mrow><mi>M</mi><mi>B</mi></mrow><mo>^</mo></mover></msub><mo>=</mo><mfrac><mrow><mi mathvariant="normal">π</mi><mo>.</mo><msup><mi mathvariant="normal">O</mi><mo>'</mo></msup><mi mathvariant="normal">M</mi><mo>.</mo><mn>2</mn><mi mathvariant="normal">α</mi></mrow><msup><mn>180</mn><mn>0</mn></msup></mfrac><mo>=</mo><mfrac><mrow><mi mathvariant="normal">π</mi><mo>.</mo><msup><mi mathvariant="normal">O</mi><mo>'</mo></msup><mi mathvariant="normal">M</mi><mo>.</mo><mi mathvariant="normal">α</mi></mrow><msup><mn>90</mn><mn>0</mn></msup></mfrac><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>(</mo><mn>1</mn><mo>)</mo><mspace linebreak="newline"/><msub><mi>l</mi><mover><mrow><mi>M</mi><mi>A</mi></mrow><mo>^</mo></mover></msub><mo>=</mo><mfrac><mrow><mi mathvariant="normal">π</mi><mo>.</mo><mi>OM</mi><mo>.</mo><mi mathvariant="normal">α</mi></mrow><msup><mn>180</mn><mn>0</mn></msup></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi><mo>.</mo><msup><mi mathvariant="normal">O</mi><mo>'</mo></msup><mi mathvariant="normal">M</mi><mo>.</mo><mi mathvariant="normal">α</mi></mrow><msup><mn>180</mn><mn>0</mn></msup></mfrac><mo>=</mo><mfrac><mrow><mi mathvariant="normal">π</mi><mo>.</mo><msup><mi mathvariant="normal">O</mi><mo>'</mo></msup><mi>Mα</mi></mrow><msup><mn>90</mn><mn>0</mn></msup></mfrac><mo> </mo><mo>(</mo><mn>2</mn><mo>)</mo><mspace linebreak="newline"/><mi>v</mi><mi>ì</mi><mo> </mo><mi>O</mi><mi>M</mi><mo>=</mo><mn>2</mn><msup><mi>O</mi><mo>'</mo></msup><mi>M</mi><mspace linebreak="newline"/><mi>S</mi><mi>o</mi><mo> </mo><mi>s</mi><mi>á</mi><mi>n</mi><mi>h</mi><mo> </mo><mo>(</mo><mn>1</mn><mo>)</mo><mo> </mo><mi>v</mi><mi>à</mi><mo> </mo><mo>(</mo><mn>2</mn><mo>)</mo><mo> </mo><mi>t</mi><mi>a</mi><mo> </mo><mi>c</mi><mi>ó</mi><mo>:</mo><mo> </mo><msub><mi>l</mi><mover><mrow><mi>M</mi><mi>B</mi></mrow><mo>^</mo></mover></msub><mo>=</mo><msub><mi>l</mi><mover><mrow><mi>M</mi><mi>A</mi></mrow><mo>^</mo></mover></msub></math></p>
<p> </p>
Hướng dẫn Giải Bài 75 (Trang 96, SGK Toán Hình học 9, Tập 2)