Question

in \\( \triangle a b c \\), \\( g \\) is the intersection of the three medians. if \\( f c = 40 \\), find \\( a f \\).

Explanation:

Step1: Recall the property of the median

A median of a triangle is a line segment joining a vertex to the mid - point of the opposite side.

Step2: Use the definition of the median

Since \( BF \) is a median of \( \triangle ABC \) (because \( G \) is the centroid, and centroid is the intersection of medians), by the definition of a median, if \( F \) is on \( AC \) and \( BF \) is a median, then \( AF=FC \).

Step3: Substitute the given value

Given \( FC = 40 \), so \( AF=40 \).

Answer:

\( AF = 40 \)