题目内容
(几何证明选讲选做题) 如图:PA与圆O相切于A,PCB为圆O的割线,并且不过圆心O,已知∠BPA=
, PA=
,PC=1,则圆O的半径等于 .
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7
由圆的性质PA
=PC·PB,得,PB=12,连接OA并反向延长交圆于点E,在直角三角形APD中可以求得PD=4,DA=2,故CD=3,DB=8,J记圆的半径为R,由于ED·DA=CD·DB
因此,(2R-2) ·2=3·8,解得R=7
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因此,(2R-2) ·2=3·8,解得R=7
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