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Question: A circle S<sub>1</sub> of area 36p cm<sup>2</sup> touches the coordinate axes. Another circle S<sub>...

A circle S1 of area 36p cm2 touches the coordinate axes. Another circle S2 smaller than S1 also touches the coordinate axes as well as S­1 also, then the radius of S2 is –

A

2cm

B

2\sqrt { 2 }cm

C

12 – 626 \sqrt { 2 }cm

D

18 – 12212 \sqrt { 2 } cm

Answer

18 – 12212 \sqrt { 2 } cm

Explanation

Solution

Let the radius of S2 is r

2\sqrt { 2 }r + r + 6 = 2\sqrt { 2 } 6

r = 6(2−12+1)\left( \frac { \sqrt { 2 } - 1 } { \sqrt { 2 } + 1 } \right) = 6(3 – 222 \sqrt { 2 } ) = 18 – 12212 \sqrt { 2 }