Question

In AABC, AD is a median and E is the mid-point of AD. If BE is produced to meet AC in E.
show that AF =1/3AC.

Answer 1

Given that AD is the median of the triangle ABC. E is the midpoint of AD

 

Construction: Through D draw a line parallel to BF to meet the line AC at G.

 

Since DG is parallel to EF, and E is the midpoint of AD, by converse of Midpoint Theorem, F is

 

the midpoint of AG and AF=FG....(1)

 

Since D is the midpoint and DG parallel to BF,by the converse of Midpoint Theorem, G is the midpoint of CF and FG=GC....(2)

 

From (1) and (2), we have,

 

AF=FG=GC

 

Thus, we have, AF=(1/3)AC

hope it helps..