Question

In the given figure, ABC and ADE are two triangles. If $\frac{DF}{FE}=\frac{AD}{AE}$, CD = 12 cm, AB = 21 cm and BC = 36 cm, then the length of AD is

• A. 14 cm
• B. 10 cm
• C. 7 cm
• D. 8 cm

Answer 1

The correct option is C 7 cm

Given: $\frac{DF}{FE}=\frac{AD}{AE},CD=12cm,AB=21cm$ and $BC=36cm$



Here, in ΔAED, F is a point on DE such that $\frac{DF}{FE}=\frac{AD}{AE}$.
Then by the converse of internal angle bisector theorem, AF is the bisector of interior ∠A.
Thus, in ΔABD, AC is the bisector of exterior of ∠A.
Now, the external angle bisector theorem states that the external angle bisector of a triangle divides the opposite side externally in the ratio of the sides containing the angle.
Thus, $\frac{BC}{CD}=\frac{AB}{AD}$
$\frac{36}{12}=\frac{21}{AD}$
$AD=7cm$
Hence, the correct answer is option (3).