The incircle of the acute-angled triangle ABC is tangent to the sides AB,BC,CA at points C1,A1,B1, respectively, and I is the incenter. Let the midpoint of side BC be M. Let J be the foot of the altitude drawn from M to C1B1. The tangent drawn from B to the circumcircle of △BIC intersects IJ at X. If the circumcircle of △AXI intersects AB at Y, prove that BY=BM. geometryAZE SENIOR NATIONAL MO