Question

在△ABC中,∠C=90°,AC=4,BC=3,O是AD上一点,且AO:OB=2:5,当AP=___,能使△OPQ与△C

Answer 1

1)OH⊥AC,BC⊥AC,则⊿AOH∽⊿ABC,OH/BC=AO/AB,即OH/3=2/(2+5),OH=6/7;

(2)①PO垂直PQ,则∠OPH+∠CPQ=90°;

又∠CQP+∠CPQ=90°.故∠OPH=∠CQP;

又∠PHO=∠C=90°.所以：△POH∽QPC

②AH/AC=AO/AB,即AH/4=2/7,AH=8/7,PH=X-8/7.

△POH∽QPC,则OH/PC=PH/CQ,即(6/7)/(4-X)=(X-8/7)/Y.

得:y=(-7/6)x²+6x-16/3.(8/7