MEMO 2008 ekipno problem 7


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28. travnja 2012.
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Let ABC be an acute-angled triangle. Let E be a point such E and B are on distinct sides of the line AC, and D is an interior point of segment AE. We have \angle ADB = \angle CDE, \angle BAD = \angle ECD, and \angle ACB = \angle EBA. Prove that B, C and E lie on the same line.
Izvor: Srednjoeuropska matematička olimpijada 2008, ekipno natjecanje, problem 7