2009 OIM Problems/Problem 4

Problem

Let $ABC$ be a triangle with $AB \ne AC$ . Let $I$ be the incenter of $ABC$ and $P$ the other point of intersection of the exterior bisector of angle $A$ with the circumcircle of $ABC$ . The line $PI$ intersects for the second time the circumcircle of $ABC$ at point $J$ . Show that the circumcircles of triangles $JIB$ and $JIC$ are tangent to $IC$ and $IB$ , respectively.