A Segment Through the Centroid

Problem

In $\triangle ABC$ , points $M$ and $N$ lie on the sides $AB$ and $AC$ respectively, and satisfy

\frac{BM}{MA}+\frac{CN}{NA}=1.

Prove that the segment $MN$ passes through the centroid of $\triangle ABC$ .

Answer

Solution

Difficulty	7/10
Topics	Triangle Geometry, vectors

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