Question 29
The altitudes of an acute-angled triangle $ABC$ intersect at point $H$. The tangent at point $A$ to the circumcircle of triangle $AHB$ intersects the line $CH$ at point $K$. The tangent at point $A$ to the circumcircle of triangle $AHC$ intersects the line $BH$ at point $L$. Prove that the points $B$, $C$, $K$, $L$ lie on the same circle.