Let $M$ be the midpoint of the internal bisector $AD$ of $\triangle ABC$.Circle $\omega_1$ with diameter $AC$ intersects $BM$ at $E$ and circle $\omega_2$ with diameter $AB$ intersects $CM$ at $F$.Show that $B,E,F,C$ are concyclic.
Source: Ukrainian National Math Olympiad 4th round
Tags: geometry unsolved, geometry
Let $M$ be the midpoint of the internal bisector $AD$ of $\triangle ABC$.Circle $\omega_1$ with diameter $AC$ intersects $BM$ at $E$ and circle $\omega_2$ with diameter $AB$ intersects $CM$ at $F$.Show that $B,E,F,C$ are concyclic.