Question

IN A ∆ABC ,E is mid point of the median AD and BE produced meets side AC at point Q.show that

BE:EQ = 3:1​

Answer 1

Step-by-step explanation:

ANSWER

given:-

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