MathDB
Centroids Coincide

Source: RMO Mumbai 2016, P5

October 11, 2016
geometrycircumcircle

Problem Statement

Let ABCABC be a triangle with centroid GG. Let the circumcircle of triangle AGBAGB intersect the line BCBC in XX different from BB; and the circucircle of triangle AGCAGC intersect the line BCBC in YY different from CC. Prove that GG is the centroid of triangle AXYAXY.
Back to ProblemsView on AoPS