Question 113
Segment $BD$ is an angle bisector in a triangle $ABC$ (point $D$ lies on segment $AC$). Line $BD$ intersects the circumcircle $\Omega$ of triangle $ABC$ at points $B$ and $E$. Circle $\omega$ with diameter $DE$ intersects $\Omega$ at points $E$ and $F$. Prove that the line symmetrical to $BF$ with respect to $BD$ contains a median of triangle $ABC$.
(L. Emelyanov)
(L. Emelyanov)