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circumcenter O equiditsant from AB,AC iff OM//BC, M is centroid

Source: 2004 Oral Moscow Geometry Olympiad grade 10 p4

October 28, 2020
geometryCentroidCircumcenterequal segments

Problem Statement

In triangle ABCABC, MM is the intersection point of the medians, OO is the center of the inscribed circle. Prove that if the line OMOM is parallel to the side BCBC, then the point OO is equidistant from the sides ABAB and ACAC.
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