Question 110
An acute triangle $ABC$ is inscribed in the circle with center $O$. We construct the altitude $AD$ ($D \in BC$) and the bisector $AE$ ($E \in BC$), which meets the circle at the point $F$. Denote by $L$ the intersection of the line $AO$ with the circle. Prove that the lines $FD$ and $LE$ intersect on the circumcircle of triangle $ABC$.
