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

In the follow...

Question

In the following figure, in $△ P Q R,$ seg $R S$ is the bisector of $∠ P R Q, P S = 3, S Q = 9, P R = 18$ . Find $Q R$

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Solution

Given: $R S$ is the bisector of $∠ P R Q$
$P S = 3, S Q = 9, P R = 18$
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.
$\frac{P Q}{Q R} = \frac{P S}{S Q}$
$= \frac{18}{Q R} = \frac{3}{9}$
$Q R = \frac{18 \times 9}{3} = 54$

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