Question

In a $△ABC$, $AD$ is a median and $E$ is mid-point of median $AD$. A line through $B$ and $E$ meets $AC$ at point $F$. Is $AC=3AF$? If True then enter 1 else if False enter 0.

Answer 1

Given: $△ABC$, E is mid point of median AD.
Construction: Draw $DG\parallel BF$
In $△ADG$, $EF\parallel DG$ and E is mid point of AD
Hence, F is mid point of AG (Mid point theorem)
or, $AF=FG$...(I)
In $△BCF$, $DG\parallel BF$ and D is mid point of BC
Therefore, G is mid point of CF (Mid point theorem)
or, $FG=GC$...(II)
From I and II
$AF=FG=GC$
Since, $AC=AF+FG+GC$
Hence, $AC=3AF$