Question

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



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Answer 1

Answer:

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

Also, BE produced meets AC at F.

We have AC = 10. 5cm , then we need to find AF.

Through D draw DK || BF.

In ΔADK, E is the mid-point of AD and EF || DK.

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

AF = FK…… (i)

In ,ΔBCFD is the mid-point of BC and BF || DK.

KC = FK…… (ii)

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

AF = FK , AF = KC…… (iii)

Now,

AC = AF +FK + KC

AC = AF + FK + KC

From (iii) equation, we get:

AC = AF + AF + AF

AC = 3AF

AF=13AC …… (iv)

We have AC = 10.5cm .Putting this in equation (iv), we get:

AF=13(10.5cm)

AF = 3.5cm