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AP is perpendicular to PC

Source: China TST 2011 - Quiz 1 - D2 - P1

May 19, 2011

Problem Statement

Let one of the intersection points of two circles with centres O1,O2O_1,O_2 be PP. A common tangent touches the circles at A,BA,B respectively. Let the perpendicular from AA to the line BPBP meet O1O2O_1O_2 at CC. Prove that AP⊥PCAP\perp PC.
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