Question 69
Let $B H$ be the altitude from the vertex $B$ to the side $A C$ of an acute-angled triangle $A B C$. Let $D$ and $E$ be the midpoints of $A B$ and $A C$, respectively, and $F$ the reflection of $H$ across the line segment $E D$. Prove that the line $B F$ passes through the circumcenter of $\triangle A B C$.