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  • In the given figure, AD is the bisector of ∠A. If AB = 9 cm, AC = 12 cm, and BC = 14 cm, then find the length of CD (in cm). <img alt="" src="https://cdn.entrance360.com/media/uploads

In the given figure, AD is the bisector of ∠A. If AB = 9 cm, AC = 12 cm, and BC = 14 cm, then find the length of CD (in cm).

Option: 1

6


Option: 2

7


Option: 3

8


Option: 4

9


Answers (1)

best_answer

In triangle ABC, AD is the bisector of the angle CAB

Given that AB = 9 cm, AC = 12 cm, and BC = 14 cm

Let BD = x, and CD = 14 - x

From the concept of angle bisector theorem

\\ \frac{BD}{DC}=\frac{AB}{AC}\Rightarrow \frac{x}{14-x}=\frac{9}{12}\\\Rightarrow 4x=42-3x\\\Rightarrow x=6\;cm

CD = 14 - 6 = 8 cm

Posted by

Divya Prakash Singh

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