MEMO 2009 ekipno problem 5


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28. travnja 2012.
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Let ABCD be a parallelogram with \angle BAD = 60 and denote by E the intersection of its diagonals. The circumcircle of triangle ACD meets the line BA at K \ne A, the line BD at P \ne D and the line BC at L\ne C. The line EP intersects the circumcircle of triangle CEL at points E and M. Prove that triangles KLM and CAP are congruent.
Izvor: Srednjoeuropska matematička olimpijada 2009, ekipno natjecanje, problem 5