KöMaL problem A, 2024

Geometry Difficulty 7.0 National Olympiad, round 2 Prove it Hungary

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.

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