ILL 1986 Problem 23

Let $I$ and $J$ be the centers of the incircle and the excircle in the angle $BAC$ of the triangle $ABC$ . For any point $M$ in the plane of the triangle, not on the line $BC$ , denote by $I_M$ and $J_M$ the centers of the incircle and the excircle (touching $BC$ ) of the triangle $BCM$ . Find the locus of points $M$ for which $II_MJJ_M$ is a rectangle.