SHARYGIN 2022 Problem 5

Let the diagonals of cyclic quadrilateral $ABCD$ meet at point $P$ . The line passing through $P$ and perpendicular to $PD$ meets $AD$ at point $D_1$ , a point $A_1$ is defined similarly. Prove that the tangent at $P$ to the circumcircle of triangle $D_1PA_1$ is parallel to $BC$ .