如图,AB是⊙O的直径,弦CD⊥AB于点E,点P在⊙O上,PB与CD交于点F,∠PBC=∠C.(1)求证:CB∥PD;(2)
如图,AB是⊙O的直径,弦CD⊥AB于点E,点P在⊙O上,PB与CD交于点F,∠PBC=∠C.(1)求证:CB∥PD;(2)若∠PBC=22.5°,⊙O的半径R=2,求劣...
如图,AB是⊙O的直径,弦CD⊥AB于点E,点P在⊙O上,PB与CD交于点F,∠PBC=∠C.(1)求证:CB∥PD;(2)若∠PBC=22.5°,⊙O的半径R=2,求劣弧AC的长度.
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千羊血梦0V
2015-01-04
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(1)证明见解析;(2) ![](https://iknow-pic.cdn.bcebos.com/dcc451da81cb39dbe594d6e4d3160924ab18302f?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) . |
试题分析:(1)先根据同弧所对的圆周角相等得出∠PBC=∠D,再由等量代换得出∠C=∠D,然后根据内错角相等两直线平行即可证明CB∥PD; (2)先由垂径定理及圆周角定理得出∠BOC=2∠PBC=45°,再根据邻补角定义求出∠AOC=135°,然后根据弧长的计算公式即可得出劣弧AC的长度. 试题解析:(1)∵∠PBC=∠D,∠PBC=∠C, ∴∠C=∠D, ∴CB∥PD; (2)∵AB是⊙O的直径,弦CD⊥AB于点E, ∴ ![](https://iknow-pic.cdn.bcebos.com/d0c8a786c9177f3e52464dbf73cf3bc79f3d5615?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) , ∵∠PBC=∠C=22.5°, ∴∠BOC=∠BOD=2∠C=45°, ∴∠AOC=180°-∠BOC=135°, ∴劣弧AC的长为: ![](https://iknow-pic.cdn.bcebos.com/34fae6cd7b899e5151da8ba641a7d933c8950d2f?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) . 【考点】1.垂径定理;2.圆周角定理;3.弧长的计算. |
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