## perp

Let $ABC$ be a triangle, $D,L,K$ is a point on $BC,CA,AB$
Circumcircle of triangle $LDC$ cuts circumcircle of triangle $KBD$ at $E(E \neq D)$
$KD$cuts $EB$at $M$
$LD$ cuts $EC$ at $N$
Suppose that $O$ is center of circumcircle of triangle $EBC$
Prove that $AO \perp MN$