Question 3
Let $ABCD$ be a cyclic convex quadrilateral with circumcircle $\Gamma$. Let $E=AC\cap BD$, let $L$ be the center of the circle tangent to sides $AB,BC,CD$, and let $M$ be the midpoint of the arc $BC$ of $\Gamma$ not containing $A,D$. Prove that the excenter of triangle $BCE$ opposite $E$ lies on $LM$.
