Question 89
Let $O$ be the circumcenter of acute triangle $ABC$, and let $AO$ meet $BC$ at $D$. From $D$ draw the rays perpendicular to $AB$ and $AC$, meeting those sides at $E,F$ and the circumcircle at $K,L$, respectively. Prove that if $K,E,F,L$ are concyclic, then $AB=AC$.