SSC CGL 18 Aug 2021 Shift 3 Paper

Question : 60 of 100

Marks: +1, -0

In a right angled

△ A B C

, the lengths of the sides containing the right angle are

5 {cm}

and

12 {cm}

respectively. A circle is inscribed in the

△ A B C

. What is the radius of the circle (in

{cm})

Solution:

Given, perpendicular

=12 {cm}

Base

=5 {cm}

By pythagoras theorem,

(\;\text " Hypotenuse "\;)^{2}=(P)^{2}+(B)^{2}

⇒ \;\; (H)^{2}=(12)^{2}+(5)^{2}=144+25

⇒ \;\; (H)^{2}=169

H=13 {cm}

Formula of in radius of circle inscribed in

△ A B C

=\;{\;\text " (Perpendicular "\;+\;\text " Base "\;-\;\text " Hypotenuse) "\;}/{2}

=\;{12+5-13}/{2}=\;{4}/{2}

∴

Radius

=2 {cm}

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