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\because \angle BAP =\angle PBC
\therefore \angle BAP+\angle ABP=90^{\circ}
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隐藏圆出现！因为圆的直径对的圆周角就是直角！
画出隐藏圆吧
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求CP的最小值，就是构建一个包含这条边的一个三角形，比如 \triangle OPC,则CP>=OC-OP
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OP是定值，则OC最短即可
