Problem

Source: 2019 NZMO Round 2 p1

Tags: geometry, angle bisector, right angle



Let X be the intersection of the diagonals AC and BD of convex quadrilateral ABCD. Let P be the intersection of lines AB and CD, and let Q be the intersection of lines PX and AD. Suppose that ABX=XCD=90o. Prove that QP is the angle bisector of BQC.