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4

Part of 2003 Oral Moscow Geometry Olympiad

Problems(1)

perpendicularity wanted, incenter, centroid, touchpoints with incircle, CA'= AB

Source: 2003 Oral Moscow Geometry Olympiad grade 9 p4

10/26/2020
In triangle ABCABC, MM is the point of intersection of the medians, OO is the center of the inscribed circle, A′,B′,C′A', B', C' are the touchpoints with the sides BC,CA,ABBC, CA, AB, respectively. Prove that if CA′=ABCA'= AB, then OMOM and ABAB are perpendicular.
PS. There is a a typo
geometryincenterCentroidperpendicular