CAT Exam Model Paper 1 with solutions for free online practice

Question : 96 of 100

Marks: +1, -0

ABCD is a square, in which a circle is inscribed touching all the sides of square. In the four corners of square, 4 smaller circles of equal radii are drawn, containing maximum possible area. What is the ratio of the area of larger circle to that of sum of the areas of four smaller circles?

1 :(68 - 48 $√2$ )
1: 17 $√2$
3 : (34 - 12 $√2$ )
None of these

Validate

Solution:

(a)

OX = XB = BY = OY =OP
Let OX = R (radius of the larger circle) then OB= R

√2

Similarly PQ = MQ = QR = r
(radius of the smaller circle)
then BQ = r

√2

∴ BP = r + r

√2

and BP =OB −OP = R

√2

− R
R

√2

− R = r + r

√2

√2

− 1) = r(

√2

+ 1)
⇒ r = R(

√2

− 1)

^2

r = R(3 − 2

√2

)
∴

{ { \Area \of \large \circle } }/ { { \Area \of \smaller \circle } } = { π R ^ { 2 } } /{ 4 π r ^ { 2 } }

= { R ^ { 2 } }/ { 4 ( 3 - 2 √ { 2 } ) ^ { 2 } R ^ { 2 } } = { 1 } /{ 4 ( 17 - 12 √{ 2 } ) }

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