IMO Shortlist 1995 problem G8

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Dodao/la: arhiva
2. travnja 2012.
Suppose that ABCD is a cyclic quadrilateral. Let E = AC\cap BD and F = AB\cap CD. Denote by H_{1} and H_{2} the orthocenters of triangles EAD and EBC, respectively. Prove that the points F, H_{1}, H_{2} are collinear.

Original formulation:

Let ABC be a triangle. A circle passing through B and C intersects the sides AB and AC again at C' and B', respectively. Prove that BB', CC' and HH' are concurrent, where H and H' are the orthocentres of triangles ABC and AB'C' respectively.
Izvor: Međunarodna matematička olimpijada, shortlist 1995