Question

如图,圆o是rt 三角形的外接圆,角abc =90

Answer 1

(1)连接OB,OP.∵OB=OA,PB=PA,∴A,B关于OP对称.

∴将图形沿OP对折后,∠OAP与∠OBP重合.∴∠OBP=∠OAP=90º.∴PB是圆O的切线.

(2)设AB交OP于D,∵OD∥CB,∴∠C=∠AOD.∴RtΔOAP∽RtΔCBA.∴CB/CA=AO/OP.

设半径为OA=r,则AC=2r,由勾股定理得OP=√(r²+3).∴1/2r=r/√(r²+3).

得(4r²+3)(r+1)(r-1)=0.∴r=1.