The figure below shows a triangle ABC. Circle of diameter AC
intersects AB and
BC at D and E, respectively. C1 is the
of triangle ABC
and C2 is the nine-point circle of triangle DBE. Circles C1 and C2
intersect at F and G. M is the midpoint of BD and BF extended intersects circle
C1 at H. Prove that the points A, M, F, and H are concyclic.