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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 =
Options
3 cm
3.5 cm
2.5 cm
5 cm
Solution
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 = 1/3 AC` …… (iv)
We have AC = 10.5cm .Putting this in equation (iv), we get:
`AF = 1/3(10.5cm)`
AF = 3.5cm
Hence the correct choice is (b).
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