MEMO 2015 ekipno problem 5


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28. kolovoza 2018.
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Let ABC be an acute triangle with |AB| > |AC|. Prove that there exists a point D with the following property: whenever two distinct points X and Y lie in the interior of ABC such that the points B, C, X, and Y lie on a circle and |\angle{AXB}| - |\angle{ACB}|  =|\angle{CYA}| - |\angle{CBA}| holds, the line XY passes through D.

Izvor: Srednjoeuropska matematička olimpijada 2015, ekipno natjecanje, problem 5