MathDB

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.

Problem Statement