Problem

Source: Ukraine 1997 grade 10

Tags: geometry, parallelogram, geometry unsolved



In a parallelogram $ ABCD$, $ M$ is the midpoint of $ BC$ and $ N$ an arbitrary point on the side $ AD$. Let $ P$ be the intersection of $ MN$ and $ AC$, and $ Q$ the intersection of $ AM$ and $ BN$. Prove that the triangles $ BDQ$ and $ DMP$ have equal areas.