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In a $\triangle$ ABC, it is given that AD is the internal bisector of $\angle A$ . If AB = 10 cm, AC = 14 cm and BC = 6 cm, then CD =?
Option: 1
3 cm

Option: 2
2.5 cm

Option: 3
2 cm

Option: 4
3.5 cm

Answers (1)

best_answer

Using Angle Bisector

$\frac{B D}{D C}=\frac{A B}{A C}$

$\\ \frac{6-x}{x}=\frac{10}{14} \\ \\\frac{6-x}{x} = \frac{5}{7}$

$\\5 x=7(6-x) \\ 5 x=42-7 x \\ 5 x+7 x=42$

$5 x+7 x =42 \Rightarrow x=3.5$

$x=3.5$

Posted by

Pankaj Sanodiya

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