Question

AD is a median of $\Delta ABC$ .E is the mid-point of AD. BE is joined and produced to meet AC at F.If $AC=6cm$ ,what is the length of AF?

Answer 1

$DrawDG\parallel BF$

$AD$ is mention and $E$ is mid-point of $AD$

$\Rightarrow AE=ED$

By converse of mid-point theorem

$F$ is mid-point of $AGandAF=FG--\left(1\right)$

Similarly, In $BCF$$D$ is midpoint of $BC\&DC\parallel BF$

$G$ is midpoint of $CAandFG=GC--\left(2\right)$

$by\left(1\right)and\left(2\right)AF=FG=GC---\left(3\right)$

From figure, $AF+FG+GC=AC$

$3AF=AC$

$AF=\frac{1}{3}\times AC$

$AF=\frac{1}{3}\times 6$

$AF=2cm$