In cyclic quadrilateral ABCD, let E, F, G, H be the orthocenters of triangles BCD, CDA, DAB, ABC, respectively. Prove that EFGH is cyclic.

Progress

So far, found that if E is orthocenter of BCD and F is orthocenter of CDA, then EF||AB.

• What have you attempted till now? – Singhal Dec 7 '14 at 6:51
• I think I should solve that: – user198223 Dec 7 '14 at 6:56
• If E is orthocenter of BCD and F is orthocenter of CDA, $EF || AB$. – user198223 Dec 7 '14 at 6:58
• @user198223: You're most of the way there! If the sides of the orthocenter quadrilateral are parallel to those of the original quadrilateral, then how do the corresponding angles of the two quads compare? – Blue Dec 7 '14 at 7:28