Let Γ1 and Γ2 be two different circles with the radius of same length and centers at points O1 and O2, respectively. Circles Γ1 and Γ2 are tangent at point P. The line ℓ passing through O1 is tangent to Γ2 at point A. The line ℓ intersects Γ1 at point X with X between A and O1. Let M be the midpoint of AX and Y the intersection of PM and Γ2 with Y=P. Prove that XY is parallel to O1O2. geometryparallelequal circles