Question 33
Let $ABC$ be an acute triangle and $M$ be the midpoint of $AB$. Let $K$ be a point such that $KB$ intersects the line $AC$, $\angle KMC = 90^\circ$ and $\angle KAC = 180^\circ - \angle ABC$. The tangent line to the circumcircle of triangle $ABC$ at $A$ intersects line $CK$ at $E$. Prove that the reflection of line $BC$ with respect to $CM$ passes through the midpoint of $ME$.