17) Let $G$ be the centroid of triangle $ABC$. Knowing that $AB < AC < BC$, which of the triangles $GAB$, $GAC$, $GBC$ has the maximum area?
(A) $GAB$
(B) $GAC$
(C) $GBC$
(D) they all have the same area

(E) it depends on the lengths of the sides of $ABC$.
17) The answer is (D).

We know that in every triangle, the centroid divides each median into two segments that are in the ratio $2: 1$.

This means that the height of triangle $G A B$ relative to side $A B$ is $1 / 3$ of the height of triangle $A B C$ relative to side $A B$, and thus the area of triangle $G A B$ is $1 / 3$ of the area of triangle $A B C$.

The same applies to triangles $G B C$ and $G C A$.

Therefore, $G A B, G B C, G C A$ have the same area.