Question

In a triangle ABC, AD is a median and E is mid-point of median AD. A line through B and E meets AC at point F.

Prove that: AC = 3AF.

Answer 1

The required figure is shown below

For help, we draw a line DG || BF

Now from triangle ADG, DG || BF and E is the midpoint of AD

Therefore, F is the midpoint of AG, i.e; AF = FG        ...(1)

From triangle BCF, DG || BF and D is the midpoint of BC

Therefore, G is the midpoint of CF, i.e; FG = GC       …(2)

AC = AF + FG + GC

= AF + AF + AF

AC = 3AF                   ...(From (1) and (2))

Hence, proved.