MathDB
angle bisector wanted, 2 right angles given, intersections of diagonals of ABCD

Source: 2019 NZMO Round 2 p1

January 10, 2021
geometryangle bisectorright angle

Problem Statement

Let XX be the intersection of the diagonals ACAC and BDBD of convex quadrilateral ABCDABCD. Let PP be the intersection of lines ABAB and CDCD, and let QQ be the intersection of lines PXPX and ADAD. Suppose that ∠ABX=∠XCD=90o\angle ABX = \angle XCD = 90^o. Prove that QPQP is the angle bisector of ∠BQC\angle BQC.
Back to ProblemsView on AoPS