KöMaL problem A, 2015

Geometry Difficulty 6.0 National Olympiad Prove it Hungary

Let $ABCD$ be a convex quadrilateral. In the triangle $ABC$ let $I$ and $J$ be the incenter and the excenter opposite to vertex $A$ , respectively. In the triangle $ACD$ let $K$ and $L$ be the incenter and the excenter opposite to vertex $A$ , respectively. Show that the lines $IL$ and $JK$ , and the bisector of the angle $BCD$ are concurrent.
Russian problem
(5 pont)

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