Question 61
Let $ABC$ be an acute triangle inscribed in a circle $\Gamma$, with orthocenter $H$. Let $K$ lie on $\Gamma$ on the opposite side of $BC$ from $A$. Let $L$ be the reflection of $K$ across line $AB$, and $M$ its reflection across line $BC$. Let $E$ be the second intersection of $\Gamma$ and the circumcircle of $BLM$. Prove that $KH,EM,BC$ are concurrent. The orthocenter is the intersection of a triangle's altitudes.