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Byju's Answer

Standard IX

Mathematics

Every Point on the Bisector of an Angle Is Equidistant from the Sides of the Angle.

In given figu...

Question

In given figure, AD is the bisector of $∠ B A C$ . If AB=10 cm. AC=14 cm. and BC=6 cm, find BD and DC.

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Solution

Let BD=x cm. Then, DC=(6-x) cm.

Since AD is the bisector of $∠ A$ .

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

$\Rightarrow$ $\frac{10}{14} = \frac{x}{6 - x}$

$\Rightarrow$ $\frac{5}{7} = \frac{x}{6 - x}$

$\Rightarrow$ $30 - 5 x = 7 x$

$\Rightarrow$ $12 x = 30$

$\Rightarrow$ $x = \frac{5}{2} = 2.5 c m$

$\Rightarrow$ $B D = 2.5 c m$ and

$D C = (6 - x) c m = (6 - 2.5) c m = 3.5 c m$

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(vii) If AB= 3.6 cm, BC e 6 cm and BD = 32 cm, find AC.
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