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CE bisects BD in pentagon with equal angles CAB, BCA, ECD, DEC , AEC

Source: 2021 Sharygin Geometry Olympiad Finals grade VIII p7

August 2, 2021
geometryequal anglesbisects segment

Problem Statement

Let ABCDEABCDE be a convex pentagon such that angles CABCAB, BCABCA, ECDECD, DECDEC and AECAEC are equal. Prove that CECE bisects BDBD.
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