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DE+AC>2BM

Source: Saint Petersburg olympiad 2024, 10.3

September 22, 2024
geometrycircumcircle

Problem Statement

On the side BCBC of acute triangle ABCABC point PP was chosen. Point EE is symmetric to point BB onto line APAP. Segment PEPE meets circumcircle of triangle ABPABP in point DD. MM is midpoint of side ACAC. Prove that DE+AC>2BMDE+AC>2BM.
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