Question

角BAC=90度,在CB的延长线上分别取点D,E,使角DAB=角BAE=角C,求证:BD/CD=AE*AE/CE*CE

Answer 1

AD^2=BD*CD

■BD/CD=(AD/CD)^2,

■只需证:AD/CD=AE/CE,

■∠EAB=ECA,∠E公共角,△EAB∽△ECA,

■AB/AC=AE/CE,

■△ABC为Rt△,AD垂直于BC

■AD/BD=AC/AB=AD/CD.所以得证