Question

In the given figure, Suppose AB, AC and BC have lengths 13 cm, 14 cm and 16 cm respectively. If $\frac{AF}{FB}=\frac{4}{5}and\frac{CE}{EA}=\frac{10}{8}$, then find BD and DC.

• A. 7 cm and 9 cm
• B. 9 cm and 7 cm
• C. 10 cm and 6 cm
• D. 8 cm and 8 cm

Answer 1

The correct option is D 8 cm and 8 cm

Given that AB = 13 , AC = 14 and BC = 16 .
Let BD = x cm and DC = 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 $\frac{AF}{FB}=\frac{4}{5}and\frac{CE}{EA}=\frac{10}{8}$ in (1),
we have, $\frac{4}{5}\times \frac{10}{8}\times \frac{x}{y}=1$
$\frac{x}{y}\times \frac{1}{1}=1$
Hence, x = y ... (2)
BC = BD + DC = 16 so, x + y = 16 ... (3)
From (2), using x = y in (3),
we get, y + y = 16
2y = 16 then y = 8
Substitute y = 8 in (3) we get, x = 8 . Hence BD = 8 cm , DC = 8 cm.