Question 51
Draw median $AM$ and bisector $AL$ of a scalene triangle $ABC$. Tangent lines of circumcircle of the triangle $ABC$ at points $B$, $C$ intersect at point $T$ and line $AT$ intersects the circumcircle at point $K$ which is different from $A$. The line $AM$ intersects circumcircle of the triangle $AKL$ at point $P$. Prove that $\angle APH = 90^\circ$, where $H$ is orthocenter of the triangle $ABC$.