Question

如图已知AB是圆O的直径点C在圆O上过点C的直线与AB的延长线交于点pAC=PC角COB=2角PCB

急

Answer 1

AC=PC,∠CAP=∠P,
OA=OC,∠OAC=∠OCA,即∠CAP=∠OCA=∠P,
∠COB=∠CAP+∠OCA=2∠P,
角COB=2角PCB,∠PCB=0.5∠COB=∠P,
∠CBO=∠PCB+∠P=2∠P,
OC=OB,∠CBO=∠BCO=2∠P=∠COB,三角形COB为等边三角形,
∠BCO=2∠P=60°,∠P=30°;
∠PCO=∠BCO+∠PCB=2∠P+∠P=60°+30°=90°;
故PC是○O的切线;