Question 102
Let $A B C$ be a triangle with orthocenter $H$. Let $P$ be any point of the plane of the triangle. Let $\Omega$ be the circle with the diameter $A P$. The circle $\Omega$ cuts $C A$ and $A B$ again at $E$ and $F$, respectively. The line $P H$ cuts $\Omega$ again at $G$. The tangent lines to $\Omega$ at $E, F$ intersect at $T$. Let $M$ be the midpoint of $B C$ and $L$ be the point on $M G$ such that $A L$ and $M T$ are parallel. Prove that $L A$ and $L H$ are orthogonal.