如图,AB是圆O的直径,点P在AB的延长线上,弦CE交AB于点D,连结OE,AC,已知∠POE=2∠CAB,∠P=∠E.
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连接AE

∠POE=∠OAE ∠OEA=2∠OAE

∠POE=2∠CAB

∠OAE=∠CAB

弧BC=弧BE

AB是直径

CE⊥AB

(2)连接OC

∠P=∠E=∠OCE

∠P ∠PCD=90°

∠P ∠OCE=90°

PC是切线

(3)PC²=PB×PA=9(9 6x)

设OD=x,BD=2x,AB=6x

DC²=2x×4x=8x²

PC²=CD² PD²=8x² (9 2x)²

9(9 6x)=8x² (9 2x)²

x=1.5

半径=3x=4.5

tan∠APC=CD/PD=√2/4

=∠∠∠