A Triangle and Intersecting Segments

Question

Let $D, E, F$ be the centres of the sides $BC, AC, AB$ of a triangle $ABC$. How do I show that the segments $AD, BE, CF$ intersect at a common point that divides each of them in the ratio $2 : 1$.

Any hints,

Thanks

Answer 1

Hint :

$1>$ Check the definition of the centroid of a Triangle

$2>$ Check in what ratio the cetroid divies the lines (in question) .