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Convex pentagon

Source: MEMO 2017 I3

August 25, 2017
geometry

Problem Statement

Let ABCDEABCDE be a convex pentagon. Let PP be the intersection of the lines CECE and BDBD. Assume that ∠PAD=∠ACB\angle PAD = \angle ACB and ∠CAP=∠EDA\angle CAP = \angle EDA. Prove that the circumcentres of the triangles ABCABC and ADEADE are collinear with PP.
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