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CAT 1999 — QA Question 13

Basics of QuadrilateralsEasy

The figure below shows two concentric circles with centre O. PQRS is a square inscribed in the outer circle. It also circumscribes the inner circle, touching it at points B, C, D and A. What is the ratio of the perimeter of the outer circle to that of polygon ABCD?

Answer & solution

  • A

    π4

  • B

    3π2

  • π2

  • D

    π

Solution

Let the radius of the outer circle be OQ = x.

Hence, perimeter of the circle = 2πx

But OQ = BC = x (diagonals of the square BQCO)

Perimeter of ABCD = 4x

Hence, ratio = 2πx4x=π2.

Hence, option (c).

CAT 1999 QA Q13: The figure below shows two concentric circles with centre O. PQRS is a square inscribed in the outer circle. I — Solution | TheCATExam