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

In the follow...

Question

In the following figure, in $△ P Q R, s e g R S$ is the bisector of $∠ P R Q, P S = 4, S Q = 10, P R = 12$ . Find $Q R$ .

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Solution

Given: $R S$ is the bisector of $∠ P R Q$ .
$P S = 4, S Q = 10, P R = 12$
To find: $Q R = ?$
In $P R Q, R S$ is the bisector of $∠ P R Q$ .
By the property of angle bisector of a triangle.
$\frac{P R}{Q R} = \frac{P S}{S Q}$
$\frac{12}{Q R} = \frac{4}{10}$
$Q R = \frac{12 \times 10}{4} = 30$ .

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