MathDB

3

Part of 2023 Mexico National Olympiad

Problems(1)

Quadrilateral geo

Source: Mexico 2023/3

11/8/2023
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.
geometry2023P3Mexico