Question

AB是圆O的直径,P是圆O上一点（不与A,B相交）,过点P的直线PC直线AB相交于点C,设角PAB等于X°（X≠45°

Answer 1

y满足关系 y+2X=90°时,PC是圆O的切线.

如图

∵AB是直径,P点在圆周上.

∴ ∠ APB=90°

∵ PC切于圆O

∴ ∠OPC=90°

∴ ∠CPB+ ∠BPO= ∠BPO+ ∠APO, ∠CPB= ∠APO=∠OAP=X

∠ABP= 90°-X

∠ABP=∠BCP +∠CPB=y+X

90°-X=y+X

y+2X=90°