如图在rt△abc中∠c=90度,AD平分∠CAB,CD=3,BD=4,求AD的长

∵AD平分∠BAC
∴AC/AB=CD/BD=3/4
设AC=x,AB=4/3x
∵∠C=90°,BC=3+4=7
根据勾股定理
AB^2-AC^2=BC^2
16/9x^2-x^2=49
x^=63
AD^2=AC^+CD^2=63+9=72
AD =6√2