IMO 2016 Shortlist G6
Let ABCD be a convex quadrilateral with ∠ABC = ∠ADC < 90◦ . The internal angle bisectors of ∠ABC and ∠ADC meet AC at E a...
Category: Geometry
Problem
Let ABCD be a convex quadrilateral with ∠ABC = ∠ADC < 90◦ . The internal angle bisectors of ∠ABC and ∠ADC meet AC at E and F respectively, and meet each other at point P. Let M be the midpoint of AC and let ω be the circumcircle of triangle BPD. Segments BM and DM intersect ω again at X and Y respectively. Denote by Q the intersection point of lines XE and Y F. Prove that PQ ⊥ AC.