MathNet 2018-part-02 — 181 problems (EN–VI) Question 92

Let $ABCD$ be an isosceles trapezoid with longer base $AB$. Let $I$ be the incenter of triangle $ABC$ and $J$ the $C$-excenter of triangle $ACD$. Prove that $IJ$ and $AB$ are parallel. (Patrik Bak)