试题与答案

Rt△ABC中,∠C=90°,若直角边AC=5,BC=12,则此三角形的内切圆半

题型:填空题

题目:

Rt△ABC中,∠C=90°,若直角边AC=5,BC=12,则此三角形的内切圆半径为________.

答案:

2

设AB、BC、AC与⊙O的切点分别为D、F、E;易证得四边形OECF是正方形;那么根据切线长定理可得:CE=CF=(AC+BC-AB),由此可求出r的长.

解:如图;

在Rt△ABC,∠C=90°,AC=5,BC=12;

根据勾股定理AB=

四边形OECF中,OE=OF,∠OEC=∠OFC=∠C=90°;

∴四边形OECF是正方形;

由切线长定理,得:AD=AE,BD=BF,CE=CF;

∴CE=CF=(AC+BC-AB);

即:r=(5+12-13)=2.

故答案为:2.

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题型:阅读理解

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