Question

如图,AD是△ABC的角平分线,且∠BAC=2∠B,求证：AC^2=CD•CB

Answer 1

∵AD平分∠BAC,∴∠BAC=2∠CAD,

∵∠BAC=2∠B,

∴∠CAD=∠B,

又∠C=∠C,

∴ΔCAD∽ΔCBA,

∴CA/CB=CD/CA,

即AC²=CD*BC.