Hướng dẫn giải Bài 91 (Trang 104 SGK Toán 9 Hình học, Tập 2)

Trong hình 68, đường tròn tâm O có bán kính R=2cm. <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mrow><mi>A</mi><mi>O</mi><mi>B</mi></mrow><mo>^</mo></mover><mo>=</mo><mn>75</mn><mo>°</mo></math>. <img class="wscnph" 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" width="138" height="171" />a) Tính sđ<math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mrow><mi>A</mi><mi>p</mi><mi>B</mi></mrow><mo>⏜</mo></mover><mo>.</mo></math> b) Tính độ dài hai cung AqB và ApB. c) Tính diện tích hình quạt tròn OAqB. Giải : a) Sđ<math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mrow><mi>A</mi><mi>p</mi><mi>B</mi></mrow><mo>⏜</mo></mover><mo>=</mo><mn>360</mn><mo>°</mo><mo>-</mo></math>sđ<math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mrow><mi>A</mi><mi>q</mi><mi>B</mi></mrow><mo>⏜</mo></mover><mo>=</mo><mn>360</mn><mo>°</mo><mo>-</mo><mn>75</mn><mo>°</mo><mo>=</mo><mn>285</mn><mo>°</mo></math> b) Độ dài cung <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mrow><mi>A</mi><mi>q</mi><mi>B</mi></mrow><mo>⏜</mo></mover></math>:                   l<math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mrow><mi>A</mi><mi>q</mi><mi>B</mi></mrow><mo>⏜</mo></mover></math>=<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>πRn</mi><mo>°</mo></mrow><mrow><mn>180</mn><mo>°</mo></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mo>,</mo><mn>14</mn><mo>.</mo><mn>2</mn><mo>.</mo><mn>75</mn><mo>°</mo></mrow><mrow><mn>180</mn><mo>°</mo></mrow></mfrac><mo>≈</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>(</mo><mi>c</mi><mi>m</mi><mo>)</mo></math> Độ dài cung <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mrow><mi>A</mi><mi>p</mi><mi>B</mi></mrow><mo>⏜</mo></mover></math>:                   l<math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mrow><mi>A</mi><mi>p</mi><mi>B</mi></mrow><mo>⏜</mo></mover></math>=<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>πRn</mi><mo>°</mo></mrow><mrow><mn>180</mn><mo>°</mo></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mo>,</mo><mn>14</mn><mo>.</mo><mn>2</mn><mo>.</mo><mn>285</mn><mo>°</mo></mrow><mrow><mn>180</mn><mo>°</mo></mrow></mfrac><mo>≈</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>(</mo><mi>c</mi><mi>m</mi><mo>)</mo></math> c) Diện tích hình quạt OAmB:                S=<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>πR</mi><mn>2</mn></msup><mi mathvariant="normal">n</mi><mo>°</mo></mrow><mrow><mn>360</mn><mo>°</mo></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mo>,</mo><mn>14</mn><mo>.</mo><msup><mn>2</mn><mn>2</mn></msup><mo>.</mo><mn>75</mn></mrow><mn>360</mn></mfrac><mo>≈</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>(</mo><mi>c</mi><msup><mi>m</mi><mn>2</mn></msup><mo>)</mo></math> Có thể dùng công thức : S=<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>l</mi><mi>R</mi></mrow><mn>2</mn></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mo>,</mo><mn>6</mn><mo>.</mo><mn>2</mn></mrow><mn>2</mn></mfrac><mo>=</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>(</mo><mi>c</mi><mi>m</mi><mo>)</mo></math>