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Problem 413: Cyclic Quadrilateral, Orthocenter, Parallelogram, Concurrency, Congruence

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. Post a comment or solution.

Cyclic quadrilateral, orthocenter, parallelogram, congruence

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