IMO Shortlist 2009 problem G4

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Dodao/la: arhiva
2. travnja 2012.
Given a cyclic quadrilateral ABCD, let the diagonals AC and BD meet at E and the lines AD and BC meet at F. The midpoints of AB and CD are G and H, respectively. Show that EF is tangent at E to the circle through the points E, G and H.

Proposed by David Monk, United Kingdom
Izvor: Međunarodna matematička olimpijada, shortlist 2009