Question

PQRS is a square. SR is a tangent (at point S) to the circle with
centre O and TR = OS. Then the ratio of area of the circle to the
area of the square is
a. π/3
b. 11/7
c. 3/π
d. 7/11

Answer 1

Answer : (a) π/3

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SOLUTION :

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Let, the side of square be x m.

So, from the definition of square :

PQ = QR = RS = SP = x

Now, let the radius of the Circle be r m

Then, from the definition of radius :

OS = OT = r

Now,

Given that :

TR = OS = OT

=> TR = OT = r

From the diagram :OR = OT + TR

=> OR = r + r=> OR = 2r

As we know that :

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Area of Circle = πr² and

Area of Square = (Side)² = x²

In triangle /_\ RSO,

OR² = OS² + RS²

=> (2r)² = (r)² + x²

=> 4r² = r² + x²

=> x² = 3r²

So, the area of square = x² = 3r²

And as we know that the area of Circle = πr²

$Now, \: the \: ratio \: of \: the \: area \: of \: Circle \: to \: the \: area \: of \: square \: = \frac{\pi {r}^{2} }{3 {r}^{2} } = \frac{\pi}{3}$

So, the ratio will be π/3

Answer 2

heyaa ......π/3 is your answer