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CAT 2005 — QA Question 3

2 CirclesEasy

Two identical circles intersect so that their centres, and the points at which they intersect, form a square of side 1 cm. The area in sq. cm of the portion that is common to the two circles is

Answer & solution

  • A

    π4

  • π2-1

  • C

    π5

  • D

    2-1

Solution

Let the two circles with centres P and Q intersect at M and N.

Quadrilateral PMQN is a square.

m ∠MPN = m ∠MQN = 90°

The area common to both the circles = 2(Area of sector P-MN – Area of ∆PMN) 

=2[(90360×π×12]-(12×12))

=π2-1

Hence, option (b).

CAT 2005 QA Q3: Two identical circles intersect so that their centres, and the points at which they intersect, form a square o — Solution | TheCATExam