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IG // AB iff CI // IO

Source: Lusophon 2019 CPLP P3

December 31, 2019
geometryparallelperpendicular

Problem Statement

Let ABCABC be a triangle with AC≠BCAC \ne BC. In triangle ABCABC, let GG be the centroid, II the incenter and O Its circumcenter. Prove that IGIG is parallel to ABAB if, and only if, CICI is perpendicular on IOIO.
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