Question

如图在△abc中∠c=90°ac=4,bc=3,o是ab上一点,ao=2,oh⊥ac,垂足为H,点p,q分别在ac,bc

Answer 1

勾股 AC=4;BC=3 =>AB=5

∠A=∠A;∠C=∠AOP=90° =>△AOP~△ACB(aa)

=>AO:AC=2:4=AP:AB=AP:5=OP:CB=OP:3 => AP=5/2; OP=3/2

=> 2*△AOP=OA*OP=AP*OH=2*(3/2)=(5/2)*OH =>OH=6/5...(1)-1

AH^2=OA^2 - OH^2=4- 36/25=64/25 => AH=8/5...(1)-2

∠C=∠OHP=90度;∠CQP=∠B; ∠B=∠APO=∠HPO =>∠CQP=∠HPO

=>△POH~△QPC(aa) .(2)

CQ:CB=CP:CA=y:3=(4-x):4 => y=(12-3x)/4 =3- (3/4) x

=> y=3- 0.75x ; 0