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USAJMO problem 1: Prove 4 points are concyclic

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April 24, 2012
USA(J)MOUSAJMOgeometrycircumcircle2012 USAJMO

Problem Statement

Given a triangle ABCABC, let PP and QQ be points on segments AB‾\overline{AB} and AC‾\overline{AC}, respectively, such that AP=AQAP=AQ. Let SS and RR be distinct points on segment BC‾\overline{BC} such that SS lies between BB and RR, ∠BPS=∠PRS\angle BPS=\angle PRS, and ∠CQR=∠QSR\angle CQR=\angle QSR. Prove that P,Q,R,SP,Q,R,S are concyclic (in other words, these four points lie on a circle).
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