Let Γ1 be a circle and P a point outside of Γ1. The tangents from P to Γ1 touch the circle at A and B. Let M be the midpoint of PA and Γ2 the circle through P, A and B. Line BM cuts Γ2 at C, line CA cuts Γ1 at D, segment DB cuts Γ2 at E and line PE cuts Γ1 at F, with E in segment PF. Prove lines AF, BP, and CE are concurrent. geometryparallelogramgeometric transformationhomothetygeometry proposed