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tangent circles when centroid lies on circle of midpoints of AC,AB and C

Source: Sharygin 2011 Final 10.1

March 31, 2019
geometryorthocenterCentroidtangent circles

Problem Statement

In triangle ABCABC the midpoints of sides AC,BCAC, BC, vertex CC and the centroid lie on the same circle. Prove that this circle touches the circle passing through A,BA, B and the orthocenter of triangle ABCABC.
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