SSC CGL 20 Aug 2021 Shift 2 Paper

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Question : 73 of 100

Marks: +1, -0

Two circles of radii

18 {cm}

and 16

{cm}

intersect each other and the length of their common chord is 20

{cm}

. What is the distance (in

{cm}

) between their centres?

$4 √{14}-2 √{39}$
$4 √{10}-2 √{39}$
$4 √{10}+2 √{39}$
$4 √{14}+2 √{39}$

Solution:

Given,

A O^{'}=18 {cm}, A O=16 {cm}

Common chord

A B=20 {cm}

Then,

A M+M B=20 {cm}

A M=M B=10 {cm}

In

△ A O^{'} M

,

\;\;\; (A O^{'})^{2}=(A M)^{2}+(M O^{'})^{2}

⇒ \;\; (18)^{2}=(10)^{2}+(O^{'} M)^{2}

⇒ 324-100=(O^{'} M)^{2}

⇒ M O^{'}=√{224}

\;\; =√{2 × 2 × 2 × 14 × 2}

⇒ M O^{'}=4 √{14} {cm}

In

△ A O M

,

(A O)^{2}=(A M)^{2}+(M O)^{2}

⇒ \;\; (16)^{2}=(10)^{2}+(M O)^{2}

⇒ 256-100=(M O)^{2}

⇒ \;\; M O=√{156}=√{2 × 2 × 3 × 13}

⇒ \;\; M O=2 √{39} {cm}

∴

Distance between the centre

O O^{'} \;\; =O^{'} M+M O

\;\; =4 √{14}+2 √{39} {cm}

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