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Regional Olympiad - Republic of Srpska 2004 Grade 9 Problem 2

Source: Regional Olympiad - Republic of Srpska 2004

September 19, 2018
geometryCentroidparallelincenter

Problem Statement

Let ABCABC be a triangle, TT its centroid and SS its incenter. Prove that the following conditions are equivalent:
(1) line TSTS is parallel to one side of triangle ABCABC,
(2) one of the sides of triangle ABCABC is equal to the half-sum of the other two sides.
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