KöMaL 2026 B5556

Let $ABCD$ be a trapezoid, and let circle $k_1$ through points $A$ and $D$ be tangent to side $BC$ at an inner point. Let circle $k_2$ through points $B$ and $C$ be tangent to side $AD$ at an inner point. Prove that the line through points of intersections of the two circles passes through the intersection of the diagonals.