MEMO 2017 pojedinačno problem 3


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12. rujna 2018.
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Let ABCDE be a convex pentagon. Let P be the intersection of the lines CE and BD. Assume that \angle PAD = \angle ACB and \angle CAP = \angle EDA.
Prove that the circumcentres of the triangles ABC and ADE are collinear with P.

Izvor: Srednjoeuropska matematička olimpijada 2017, pojedinačno natjecanje, problem 3