在半径为1的圆中,长为 的弦所对的劣弧的弧长等于 。
在半径为1的圆中,长为的弦所对的劣弧的弧长等于。...
在半径为1的圆中,长为 的弦所对的劣弧的弧长等于 。
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光棍快乐1417
推荐于2016-08-12
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试题分析:利用AB= ![](https://iknow-pic.cdn.bcebos.com/241f95cad1c8a786641c75bc6409c93d70cf5049?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ,OA=OB=1,则AB 2 =OA 2 +OB 2 ,根据勾股定理的逆定理得到△AOB为直角三角形,且∠AOB=90°进而得出长度等于 ![](https://iknow-pic.cdn.bcebos.com/241f95cad1c8a786641c75bc6409c93d70cf5049?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) 的弦所对的弧长有两段分别求出即可. 如图,在⊙O中,AB= ![](https://iknow-pic.cdn.bcebos.com/241f95cad1c8a786641c75bc6409c93d70cf5049?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ,OA=OB=1, ∴AB 2 =OA 2 +OB 2 , ∴△AOB为直角三角形,且∠AOB=90°, 即长度等于 ![](https://iknow-pic.cdn.bcebos.com/241f95cad1c8a786641c75bc6409c93d70cf5049?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) 的弦所对的劣弧的弧长 ![](https://iknow-pic.cdn.bcebos.com/94cad1c8a786c917d1356d8bca3d70cf3bc75749?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) . 点评:解题的关键是熟练掌握弧长公式: ![](https://iknow-pic.cdn.bcebos.com/0e2442a7d933c8950fb0a4c9d21373f0830200b1?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ,注意在使用公式时度不带单位. |
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