...如图(1),在面积为S的△ABC中, BC=a,AC="b," AB=c,内切圆O的半径为r...

发布网友发布时间：2024-10-02 22:16

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热心网友时间：2024-10-03 03:12

（1）（2） .

试题分析：（1）如图，连接OA、OB、OC、OD，则△AOB、△BOC、△COD和△DOA都是以点O为顶点、高都是r的三角形，根据即可求得四边形的内切圆半径r.
（2）过点D作DE⊥AB于点E，分别求得AE的长，进而BE 的长，然后利用勾股定理求得BD的长；然后根据，，两式相除，即可得到的值.
试题解析：（1）如图（2），连接OA、OB、OC、OD.···················································1分
∵ ·3分
∴ ························································································4分

（2）如图（3），过点D作DE⊥AB于点E，
则

·························································6分
∵AB∥DC，∴ .
又∵ ，
∴ .即 .···········································································9分