SSC CHSL 13 Apr 2021 Shift 3 Paper

Section: Quantitative Aptitude

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Question : 60 of 100

Marks: +1, -0

A circle touches all four sides of a quadrilateral

P Q R S

. If

P Q=11 {cm}

,

Q R=12 {cm}

and

P S=8 {cm}

, then what is the length of

R S

?

$9 {cm}$
$7.3 {cm}$
$7 {cm}$
$15 {cm}$

Solution:

Given,

Let the circle touches

P Q, Q R, R S

and

S P

at

A, B, C

and

D

respectively,

∴ \;\; P A \;\; =P D, Q A=Q B, R B=R C,

S C \;\; =S D

(lengths of tangents)
Let

P A=P D=x

∴ \;\; Q A=Q B=11-x

and

S D=S C=8-x

∴ \;\; R B=R C=12-(11-x)=1+x

∴ \;\; R S=R C+C S=1+x+8-x

=9 {cm}

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