如图,AB是⊙O的直径,∠BAC=45°,AB=BC. (1)求证:BC是⊙O的切线;(2)设
如图,AB是⊙O的直径,∠BAC=45°,AB=BC.(1)求证:BC是⊙O的切线;(2)设阴影部分的面积为a,b,⊙O的面积为S,请写出S与a,b的关系式....
如图,AB是⊙O的直径,∠BAC=45°,AB=BC. (1)求证:BC是⊙O的切线;(2)设阴影部分的面积为a,b,⊙O的面积为S,请写出S与a,b的关系式.
展开
呼夜天Si
2014-12-02
·
TA获得超过152个赞
知道答主
回答量:111
采纳率:100%
帮助的人:121万
关注
(1)证明见试题解析;(2) ![](https://iknow-pic.cdn.bcebos.com/adaf2edda3cc7cd957819d6b3a01213fb90e91d0?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) . |
试题分析:(1)AB是⊙O的直径,那么求得∠ABC为90°即可; (2)设AC圆交于点D,连接BD,因为AD=BD,那么a可转移到弧BD与弦BD围成的面积,即△BCD的面积= ![](https://iknow-pic.cdn.bcebos.com/aa18972bd40735faa561e70b9d510fb30e2408ea?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ,易得△ADB的面积=△BCD的面积,那么半圆的面积= ![](https://iknow-pic.cdn.bcebos.com/962bd40735fae6cd3f2502d30cb30f2443a70fea?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ,从而得到三者的关系. 试题解析:(1)证明:∵AB=BC,∴∠CAB=∠ACB=45°.∵在△ABC中,∠ABC=180°﹣45°﹣45°=90°,∴AB⊥BC.又∵AB是⊙O的直径,∴BC是⊙O的切线. (2)设AC圆交于点D,连接BD,∵AD=BD,∴△BCD的面积= ![](https://iknow-pic.cdn.bcebos.com/aa18972bd40735faa561e70b9d510fb30e2408ea?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ,∵△ADB的面积=△BCD的面积,∴半圆的面积= ![](https://iknow-pic.cdn.bcebos.com/962bd40735fae6cd3f2502d30cb30f2443a70fea?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ,∴ ![](https://iknow-pic.cdn.bcebos.com/adaf2edda3cc7cd957819d6b3a01213fb90e91d0?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) . |
收起
为你推荐: