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Asymmetric geometry involving... NT?

Source: 2022 Bulgarian Spring Math Competition, Problem 9.2

March 27, 2022
geometrymedianCircumcenter

Problem Statement

Let △ABC\triangle ABC have median CMCM (M∈ABM\in AB) and circumcenter OO. The circumcircle of △AMO\triangle AMO bisects CMCM. Determine the least possible perimeter of △ABC\triangle ABC if it has integer side lengths.
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