\item Two circles Γ1 and Γ2 intersect at points A and B. Consider a circle Γ contained in Γ1 and Γ2, which is tangent to both of them at D and E respectively. Let C be one of the intersection points of line AB with Γ, F be the intersection of line EC with Γ2 and G be the intersection of line DC with Γ1. Let H and I be the intersection points of line ED with Γ1 and Γ2 respectively. Prove that F, G, H and I are on the same circle. geometrygeometric transformationhomothetyreflectioncyclic quadrilateralpower of a pointradical axis