Question

In AABC, point D is the centroid, and AD = 12. Find AG.BFGDАEAG =

Answer 1

In this problem we need to use the CENTROID THEOREM.

This theorem states that the CENTROID is two thirds of the distance from each vertex to the midpoint of the opposite side.

In our problem the theorem states that:

`AD=(2)/(3)AG`

Using that AD = 12, we find that:

`\begin{gathered} AD=(2)/(3)AG \\ 12=(2)/(3)AG \\ AG=(3)/(2)\cdot12=18 \end{gathered}`

The answer is: AG = 18