Question

In the given figure,Suppose AB, AC and BC have lengths 10 cm, 11 cm and 12 cm respectively. If $\frac{BD}{DC}=\frac{5}{6}and\frac{CE}{EA}=\frac{3}{10}$, then find AF and FB.

• A. 2 cm and 8 cm
• B. 8 cm and 2 cm
• C. 6 cm and 4 cm
• D. 5 cm and 5 cm

Answer 1

The correct option is B 8 cm and 2 cm

Given that AB = 10 cm , AC = 11 cm and BC = 12 cm .
Let AF = x cm and FB = y cm.

Using Ceva’s theorem, we have,
$\frac{AF}{FB}\times \frac{CE}{EA}\times \frac{BD}{DC}=1$ ... (1)
Substitute the values of $\frac{BD}{DC}=\frac{5}{6}and\frac{CE}{EA}=\frac{3}{10}$ in (1),
we have, $\frac{5}{6}\times \frac{3}{10}\times \frac{x}{y}=1$
$\frac{x}{y}\times \frac{1}{4}=1$
Hence, x = 4y ... (2)
AB = AF + FB = 10 so, x + y = 10 ... (3)
From (2), using x = 4y in (3),
we get, 4y + y = 10
5y = 10 then y = 2
Substitute y = 2 in (3) we get, x = 8 . Hence AF = 8 cm , FB = 2 cm.