如图,在⊙O中,直径AB=10,弦AC=6,∠ACB的平分线交⊙O于点D。求BC和AD的长。
如图,在⊙O中,直径AB=10,弦AC=6,∠ACB的平分线交⊙O于点D。求BC和AD的长。...
如图,在⊙O中,直径AB=10,弦AC=6,∠ACB的平分线交⊙O于点D。求BC和AD的长。
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宣卿02B
推荐于2016-12-01
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BC=8,AD= |
试题分析:在⊙O中,直径AB=10,那么 ![](https://iknow-pic.cdn.bcebos.com/279759ee3d6d55fb7e7f25946e224f4a21a4ddc3?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ,在直角三角形ABC中,由勾股定理得 ![](https://iknow-pic.cdn.bcebos.com/f603918fa0ec08fa96b940155aee3d6d54fbdac3?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ,因为弦AC=6,所以 ∠ACB的平分线交⊙O于点D, ![](https://iknow-pic.cdn.bcebos.com/ae51f3deb48f8c54be59969d39292df5e1fe7ffd?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ,因为在⊙O中,直径AB=10,那么 ![](https://iknow-pic.cdn.bcebos.com/279759ee3d6d55fb7e7f25946e224f4a21a4ddc3?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ,所以 ![](https://iknow-pic.cdn.bcebos.com/58ee3d6d55fbb2fb8e920ba04c4a20a44723dcc3?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ,弧AD所对的圆周角是 ![](https://iknow-pic.cdn.bcebos.com/b3fb43166d224f4af02020a10af790529922d1c3?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ,弧BD所对的圆周角是 ![](https://iknow-pic.cdn.bcebos.com/8d5494eef01f3a290042867c9a25bc315d607cfd?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ,因为AB是⊙O的直径,所以可得出D是弧AB的中点,AD=BD;又因为AB是⊙O的直径,所以 ![](https://iknow-pic.cdn.bcebos.com/f11f3a292df5e0feb692dab35f6034a85fdf72fd?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ,在直角三角形ABD中,由勾股定理可得 ![](https://iknow-pic.cdn.bcebos.com/6c224f4a20a44623db73f6d09b22720e0df3d7c3?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ,解得 ![](https://iknow-pic.cdn.bcebos.com/d8f9d72a6059252d3cae4eb6379b033b5ab5b9c3?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) = 点评:本题考查平分线,圆,勾股定理,本题考查平分线的性质,圆的直径所对的圆周角为直角,勾股定理的内容 |
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