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

The Angle-Bisector theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides (It may be similar or may not depending on type of triangle it divides)

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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