Question 48
Let ABC be an isosceles right triangle with right angle at B. Let M be a point of arc AC of the circle with centre B through A and C, and H its orthogonal projection onto line AB. Let I be the incenter of BHM and J its excenter in angle B (thus J is the intersection of the internal bisector at B and the external bisectors at H and M). Prove that MIAJ is a square.