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Source: 1992 National High School Mathematics League, Exam Two, Problem 1

February 27, 2020
geometrycyclic quadrilateral

Problem Statement

A1A2A3A4A_1A_2A_3A_4 is cyclic quadrilateral of ⊙O\odot O. H1,H2,H3,H4H_1,H_2,H_3,H_4 are orthocentres of △A2A3A4,△A3A4A1,△A4A1A2,△A1A2A3\triangle A_2A_3A_4,\triangle A_3A_4A_1,\triangle A_4A_1A_2,\triangle A_1A_2A_3. Prove that H1,H2,H3,H4H_1,H_2,H_3,H_4 are concyclic, and determine its center.
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