# CAT Practice : Coordinate Geometry

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Find out what shape is PQRS and assume the side of ABCD to be 2a to get further answer!

## Ratio of circumferences

Q.35: There are 2 concentric circles, one big and one small. A square ABCD is inscribed inside the big circle while the same square circumscribes the small circle. The square touches the small circle at points P, Q, R and S. Determine the ratio of circumference of big circle to the polygon PQRS.
1. π : 2
2. 2 : π
3. 2 : ${\surd 2}$
4. π : ${\surd 2}$

Choice (A). π : 2

## Detailed Solution

Let the side of the square ABCD be 2a
A line from the centre will bisect the chords AB, BC, CD and DA
Therefore AP = PB = a. Similarly for other sides too
From the above we can conclude that PQ = QR = RS = SP
PQRS is also a square!

Radius of big circle = diagonal of the square APOS = a${\surd 2}$
Circumference = 2π* a${\surd 2}$

Now we have to find the side of square PQRS
We know that radius of small circle = side of the square APOS = a

Consider triangle PSO. PS2 = OP2 + OS2
PS = a${\surd 2}$
Circumference of square with side a${\surd 2}$ = 4a${\surd 2}$
Ratio = 2π* a${\surd 2}$ : 4a${\surd 2}$
= π : 2

Correct Answer: (A). = π : 2

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Geometry is probably the most vital topic as far as CAT preparation is concerned. Geometry sets the stage for Trigonometry, Cogeo and Mensuration as well.