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CAT 1995 — QA Question 17

Basics of QuadrilateralsEasy
Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

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

  • 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.

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