As shown in the figure, it is known that BC=AC in △ABC, M is the midpoint of AB, points D, E lie on AB such that ∠DCE=∠MCB, the circumscribed circle of △BDC and the circumscribed circle of △AEC intersect at point F(different from point C), point H lies on AB such that the straight line CM bisects the line segment HF. Let the circumcenters of △HFE and △BFM be O1, O2 respectively. Prove that O1O2⊥CF.
https://cdn.artofproblemsolving.com/attachments/8/c/62d4ecbc18458fb4f2bf88258d5024cddbc3b0.jpg perpendicularperpendicularitygeometry