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S centroid if [ABS]=[BCS]=[CAS]

Source: Eotvos 1936 p2

September 10, 2024
geometryequal areasCentroid

Problem Statement

SS is a point inside triangle ABCABC such that the areas of the triangles ABSABS, BCSBCS and CASCAS are all equal. Prove that SS is the centroid of ABCABC.
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