IMO 2020 Shortlist G2

Let ABCD be a convex quadrilateral. Suppose that P is a point in the interior of ABCD such that =PAD : =PBA : =DPA “ 1 :...

IMO 2020 Shortlist G2

Category: Geometry

Problem

Let ABCD be a convex quadrilateral. Suppose that P is a point in the interior of ABCD such that =PAD : =PBA : =DPA “ 1 : 2 : 3 “ =CBP : =BAP : =BPC. The internal bisectors of angles ADP and PCB meet at a point Q inside the triangle ABP. Prove that AQ “ BQ. (Poland)