Let AB be a chord of a circle Γ and let C be a point on the segment AB. Let r be a line through C which intersects Γ at the points D,E; suppose that D,E lie on different sides with respect to the perpendicular bisector of AB.
Let ΓD be the circumference which is externally tangent to Γ at D and touches the line AB at F. Let ΓE be the circumference which is externally tangent to Γ at E and touches the line AB at G.
Prove that CA=CB if and only if CF=CG. geometryperpendicular bisector