IMO 1986 LL FRA23

Origin: FRA

Problem

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 IM and JM the centers of the incircle and the excircle (touching BC) of the triangle BCM. Find the locus of points M for which IIMJJM is a rectangle.