In triangle ABC, let ω be the excircle opposite to A. Let D,E and F be the points where ω is tangent to BC,CA, and AB, respectively. The circle AEF intersects line BC at P and Q. Let M be the midpoint of AD. Prove that the circle MPQ is tangent to ω. geometryIMO Shortlistgeometry solvedhomothetytangent circlespower of a pointexcircle