KURSCHAK 2012 Problem 1

Let $J_A$ and $J_B$ be the $A$ -excenter and $B$ -excenter of $\triangle ABC$ . Consider a chord $\overline{PQ}$ of circle $ABC$ which is parallel to $AB$ and intersects segments $\overline{AC}$ and $\overline{BC}$ . If lines $AB$ and $CP$ intersect at $R$ , prove that $$\angle J_AQJ_B+\angle J_ARJ_B=180^\circ.$$