In $△$ ABC, AB = 3 and, AC = 4 cm and AD is the bisector of $∠$ A. Then, BD : DC is —

9:16

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16:9

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3:4

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4:3

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Solution

The correct option is C
3:4

According to angle bisector theorem, the internal bisector of an angle of a triangle divided the oppposite side internally in the ratio of the corresponding sides containing the angle.

In $△ A B C$

as per the statement $\frac{A B}{A C} = \frac{B D}{D C}$ i.e. $\frac{a}{b} = \frac{c}{d}$

So, $\frac{B D}{D C}$ = $\frac{A B}{A C}$ = $\frac{3}{4}$

So, BD : DC = 3 : 4

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In a $Δ A B C$ , AD is the bisector of $∠ A$ .

(i) If AB = 6.4 cm, AC = 8 cm and BD = 5.6 cm, find DC.

(ii) If AB = 10 cm, AC = 14 cm and BC = 6 cm, find BD and DC.

(iii) If AB = 5.6 cm, BD = 3.2 cm and BC = 6 cm, find AC.

(iv) If AB = 5.6 cm, AC = 4 cm and DC = 3 cm, find BC.

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