The figure shows a cyclic quadrilateral
ABCD. The points E, F, G, and H are the orthocenters of triangles ABD,
ACD, ABC, and BCD, respectively. Prove that (1) BCFE, ABHF, AGHD, and
CDEG are parallelograms, (2) Lines AH, BF, CE, and DG are concurrent,
(3) Quadrilaterals ABCD and HFEG are congruent.
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