OIM 2009 Problem 4

Given a triangle $ABC$ of incenter $I$ , let $P$ be the intersection of the external bisector of angle $A$ and the circumcircle of $ABC$ , and $J$ the second intersection of $PI$ and the circumcircle of $ABC$ . Show that the circumcircles of triangles $JIB$ and $JIC$ are respectively tangent to $IC$ and $IB$ .