Question

已知,如图,在△ABC中,AD垂直于BC,D为垂足,AB乘以CD=AC乘以AD 求证：AB的平方=BD乘以BC

Answer 1

∵AB×CD＝AC×AD,∴AB/AC＝AD/CD.······①

∵AD⊥CD,∴tan∠C＝AD/CD.······②

由①、②,得：tan∠C＝AB/AC,∴∠BAC＝90°,∴由射影定理,得：AB^2＝BD×BC.