SSC CHSL 12 Aug 2021 Shift 3 Paper

Section: Quantitative Aptitude

Question : 66 of 99

Marks: +1, -0

Two circles with centres

O

and

P

and radii

17 {cm}

and

10 {cm}

, respectively, intersect each other at

A

and

B

. The length of the common chord

A B

16 {cm}

. What is the perimeter of the

△ O A P(

{cm})

Solution:

Given,

△ O A C

O C=√{(17)^{2}-(8)^{2}}

[ ∵

Perpendicular on chord from centre is divided the chord in two equal parts]

=√{289-64}=√{225}=15 {cm}

△ P A C

C P \;\; =√{(10)^{2}-(8)^{2}}

\;\; =√{100-64}=√{36}=6 {cm}

∴ O P \;\; =O C+C P=15+6=21 {cm}

Now, the perimeter of

∆ O A P \;\; =O A+A P+O P

\;\; =17+10+21=48 {cm}

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