Question

In ΔABC, E is the mid-point of median AD such that BE produced meets AC at F. IF AC = 10.5 cm, then AF =

(a) 3 cm

(b) 3.5 cm

(c) 2.5 cm

(d) 5 cm

Answer 1

is given with E as the mid-point of median AD.

Also, BE produced meets AC at F.

We have , then we need to find AF.

Through D draw .

In , E is the mid-point of AD and .

Using the converse of mid-point theorem, we get:

…… (i)

In , D is the mid-point of BC and .

…… (ii)

From (i) and (ii),we have:

, …… (iii)

Now,

From (iii) equation, we get:

…… (iv)

We have .Putting this in equation (iv), we get:

Hence the correct choice is (b).