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Circumcircle of RPS is tangent to BC

Source: Saudi Arabia IMO TST Day I Problem 3

July 22, 2014
geometrycircumcirclegeometry unsolved

Problem Statement

Let ABCABC be a triangle and let PP be a point on BCBC. Points MM and NN lie on ABAB and ACAC, respectively such that MNMN is not parallel to BCBC and AMPNAMP N is a parallelogram. Line MNMN meets the circumcircle of ABCABC at RR and SS. Prove that the circumcircle of triangle RPSRP S is tangent to BCBC.
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