如图,Rt△ABC的内切圆的半径为1㎝,斜边与圆O相切于点D,已知AB=5,求AD,AC的长.

问题描述:

如图,Rt△ABC的内切圆的半径为1㎝,斜边与圆O相切于点D,已知AB=5,求AD,AC的长.

∠C=90°吗?设⊙O切AC于E,切BC于F,四边形OECF是正方形,∴CE=CF=1,根据切线长相等得:AE=AD,BF=BD,∴AE+BF=AB=5,设AE=X(X>0),则BF=5-X,∴AC=X+1,BC=6-X,根据勾股定理得:(X+1)^2+(6-X)^2=25,2X^2-10X+12=0X^2-5X+6=0,...