Question

如图,三角形ADE中,角DAE=90`AC是高 B在DE延长线上,角BAE=角D,求证：BE^2/EC^2=BD/DC

Answer 1

由题目可知一些条件：

△ABE∽△ADB(AA)

△AEC∽△ACD(AA)

BE/BA=BA/BD=EA/AD

AC/CD=EC/AC=EA/AD

则BE/BA=AC/EC

∴(BE/BA):(AC/EC)=1

(BE/EC)×(AC/BA)=1

BE/EC=BA/AC BE²/EC²=BA²/AC²

BA²=BE×BD

AC²=CE×CD

BE²/EC²=(BE×BD)/(CE×CD)≠BD/CD

BE≠CE∴BE²/EC²≠BD/CD