MEMO 2011 ekipno problem 5


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28. travnja 2012.
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Let ABCDE be a convex pentagon with all five sides equal in length. The diagonals AD and EC meet in S with \angle ASE = 60^\circ. Prove that ABCDE has a pair of parallel sides.
Izvor: Srednjoeuropska matematička olimpijada 2011, ekipno natjecanje, problem 5