KöMaL problem A, 2016

Geometry Difficulty 7.0 National Olympiad, round 2 Prove it Hungary

The circle $\omega$ is inscribed in the quadrilateral $ABCD$ . The incenters of the triangles $ABC$ and $ACD$ are $I$ and $J$ , respectively. Let $T$ and $U$ be those two points on the arcs of $\omega$ , lying in the triangles $ABC$ and $ACD$ , respectively, for which the circles $ATC$ and $AUC$ are tangent to $\omega$ . Show that the line segments $AC$ , $IU$ and $JT$ are concurrent.
(5 pont)

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