MathNet 2021 — Part 10 Question 73

Let $ABC$ be a triangle, with $M$ on the side $AB$ and $N$ on the side $AC$. Suppose that $CM$ and $BN$ intersect at $D$, and that the circumcircles of $BDM$ and $BNC$ intersect again at $E$. Show that $M,N,E$ are collinear if $\angle BDM=\angle ACB$.

(Proposed by Khulan Tumenbayar)