Question

In triangle ABC, E is the mid point of median AD such that BE produced meets AC at F. if AC = 10.5 , then AF = ? ​

Answer 1

Step-by-step explanation:

AD is the median of ΔABC and E is the midpoint of AD

Through D draw DG∣∣BF

In ΔADG

E is the midpoint of AD and EF∣∣DG

By converse of midpoint theorem we have

F is midpoint of AG and AF=FG  ..............1

Similarly, in ΔBCF

D is the midpoint of BC and DG∣∣BF   

G is midpoint of CF and FG=GC ..............2

From equations 1 and 2

we will get

AF=FG=GC........3

AF+FG+GC=AC

AF+AF+AF=AC  ......... from eq 3

AF=AC

AF=(1/3)AC

AF=(1/3)*10.5

AF = 3.5