IMO Shortlist 2016 problem G6


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3. listopada 2019.
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Let ABCD be a convex quadrilateral with \angle ABC = \angle ADC < 90^{\circ}. The internal angle bisectors of \angle ABC and \angle ADC meet AC at E and F respectively, and meet each other at point P. Let M be the midpoint of AC and let \omega be the circumcircle of triangle BPD. Segments BM and DM intersect \omega again at X and Y respectively. Denote by Q the intersection point of lines XE and YF. Prove that PQ \perp AC.

Izvor: https://www.imo-official.org/problems/IMO2016SL.pdf