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Geo ineq with median

Source: St. Petersburg 2023 11.2

August 12, 2023
geometry

Problem Statement

Given is a triangle ABCABC with median BMBM. The point DD lies on the line ACAC after CC, such that BD=2CDBD=2CD. The circle (BMC)(BMC) meets the segment BDBD at NN. Show that AC+BM>2MNAC+BM>2MN.
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