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CAT 1995 — QA Question 17

Basics of QuadrilateralsEasy

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

Answer & solution

Correct answer: π 3

  • π3

  • B

    117

  • C

    3π

  • D

    711

Solution

In the given figure, the area of the circle = pr2.
To find out the area of the circle, we need to find out the length of the side of the square.
We know, OR = OT + TR = OT + OS = 2r.
In right-angled triangle ORS, OR = 2r and OS = r.
So SR2 = OR2 – OS2.
But SR2 = Area of the square = 4r2 – r2 = 3r2.
Hence, the required ratio = π3.

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CAT 1995 QA Q17: 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 — Solution | TheCATExam