KöMaL 2024 A877

Convex quadrilateral $ABCD$ is circumscribed about circle $\omega$. A tangent to $\omega$ parallel to diagonal $AC$ meets diagonal $BD$ at point $P$ outside of $\omega$. The second tangent from $P$ to $\omega$ touches $\omega$ at point $T$. Prove that $\omega$ and the circumcircle of triangle $ATC$ are tangent.