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ABC and DEF have the same centroid

Source:

October 15, 2010

geometryparallelogramsymmetrygeometry proposed

Problem Statement

The points

D,E

and

F

are chosen on the sides

BC,AC

and

AB

of triangle

ABC

, respectively. Prove that triangles

ABC

and

DEF

have the same centroid if and only if

\frac{BD}{DC} = \frac{CE}{EA}=\frac{AF}{FB}

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