Question

in $\triangle abc$, $g$ is the intersection of the three medians. if $fc = 40$, find $af$.

Explanation:

Step1: Recall the property of a median

A median of a triangle connects a vertex to the midpoint of the opposite side. So, in \(\triangle ABC\), since \(BF\) is a median (as \(G\) is the centroid, the intersection of medians), \(F\) must be the midpoint of \(AC\).

Step2: Use the midpoint property

If \(F\) is the midpoint of \(AC\), then \(AF = FC\).

Step3: Substitute the given value

We know that \(FC = 40\), so by the midpoint property, \(AF = FC = 40\).

Answer:

40