Problem

Source:

Tags: geometry, circumcircle, geometry proposed



The line passing through $B$ is perpendicular to the side $AC$ at $E$. This line meets the circumcircle of $\triangle ABC$ at $D$. The foot of the perpendicular from $D$ to the side $BC$ is $F$. If $O$ is the center of the circumcircle of $\triangle ABC$, prove that $BO$ is perpendicular to $EF$.