MEMO 2010 pojedinačno problem 3

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April 28, 2012
We are given a cyclic quadrilateral ABCD with a point E on the diagonal AC such that AD=AE and CB=CE. Let M be the center of the circumcircle k of the triangle BDE. The circle k intersects the line AC in the points E and F. Prove that the lines FM, AD and BC meet at one point.
Source: Srednjoeuropska matematička olimpijada 2010, pojedinačno natjecanje, problem 3