2020 IMO Problems/Problem 1

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Problem 1. Consider the convex quadrilateral ABCD. The point P is in the interior of ABCD. The following ratio equalities hold: ∠P AD : ∠P BA : ∠DP A = 1 : 2 : 3 = ∠CBP : ∠BAP : ∠BP C. Prove that the following three lines meet in a point: the internal bisectors of angles ∠ADP and ∠P CB and the perpendicular bisector of segment AB.

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