Question 77
Let $O$ be the circumcenter of an acute triangle $ABC$. A line perpendicular to $AO$ intersects the line segments $[AC]$ and $[AB]$ at $D$ and $E$, respectively. Let $K$ be a point on $[BC]$ which is not on the line $AO$. The line $AK$ intersects the circumcircle of triangle $ADE$ again at $L$. Let $M$ be the point symmetric to $A$ with respect to the line $DE$. Show that the points $K$, $L$, $M$, $O$ are concyclic.