MEMO 2009 pojedinačno problem 3


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28. travnja 2012.
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Let ABCD be a convex quadrilateral such that AB and CD are not parallel and AB=CD. The midpoints of the diagonals AC and BD are E and F, respectively. The line EF meets segments AB and CD at G and H, respectively. Show that \angle AGH = \angle DHG.
Izvor: Srednjoeuropska matematička olimpijada 2009, pojedinačno natjecanje, problem 3