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2022 Geo Div 2 P6

Source:

February 28, 2022
geometry

Problem Statement

A triangle △ABC\triangle ABC satisfies AB=13AB = 13, BC=14BC = 14, and AC=15AC = 15. Inside △ABC\triangle ABC are three points XX, YY, and ZZ such that:
[*] YY is the centroid of △ABX\triangle ABX [*] ZZ is the centroid of △BCY\triangle BCY [*] XX is the centroid of △CAZ\triangle CAZ
What is the area of △XYZ\triangle XYZ?
Proposed by Adam Bertelli
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