Question 3
In triangle $ABC$, let $D\in BC$ with $AD$ the internal bisector of $\angle BAC$, and let $M$ be the midpoint of $AD$. Circle $\omega_1$ with diameter $AC$ intersects $BM$ at $E$, and circle $\omega_2$ with diameter $AB$ intersects $CM$ at $F$. Prove that $B,E,F,C$ are concyclic.
