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Circles with AB and AC as diameters

Source: Central American Olympiad 2000, problem 5

August 9, 2007
trigonometry

Problem Statement

Let ABC ABC be an acute-angled triangle. C1 C_{1} and C2 C_{2} are two circles of diameters AB AB and AC AC, respectively. C2 C_{2} and AB AB intersect again at F F, and C1 C_{1} and AC AC intersect again at E E. Also, BE BE meets C2 C_{2} at P P and CF CF meets C1 C_{1} at Q Q. Prove that AP=AQ AP=AQ.
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