MathDB
Quadrilateral geo

Source: Mexico 2023/3

November 8, 2023
geometry2023P3Mexico

Problem Statement

Let ABCDABCD be a convex quadrilateral. If M,N,KM, N, K are the midpoints of the segments AB,BCAB, BC, and CDCD, respectively, and there is also a point PP inside the quadrilateral ABCDABCD such that, ∠BPN=∠PAD\angle BPN= \angle PAD and ∠CPN=∠PDA\angle CPN=\angle PDA. Show that AB⋅CD=4PM⋅PKAB \cdot CD=4PM\cdot PK.
Back to ProblemsView on AoPS