证明:∠ACB=∠ADC=90°;∠A=∠A.
则⊿ADC∽⊿ACB,AD/AC=AC/AB,AC^2=AD*AB;
同理可证:⊿BDC∽⊿BCA,BC/AB=BD/BC,BC^2=BD*AB.
所以,AC^2:BC^2=(AD*AB):(BD*AB)=AD:BD.