Quantitative Aptitude – Circles – Two circles P and Q, each of radius 2

XAT 2021 Exam Paper – Quantitative Aptitude – Circles – Two circles P and Q, each of radius 2

Q. Two circles P and Q, each of radius 2 cm, pass through each other’s centres. They intersect at points A and B. A circle R is drawn with diameter AB. What is the area of overlap (in square cm) between the circles R and P?

1. 8Ï€/3
2. 17Ï€/6 – √3
3. 8Ï€/3 – 2√3
4. 17Ï€/6 – 2√3
5. 13Ï€/3 – √3

Answer: 17Ï€/6 – √3

Solutions:
From the question , following figure can be made,

AB is the diameter of circle R.
Radius AC of circle R = √(2^2-1^2 )=√3
Thus common area of circle P and R = area of semi cirle of circle R + Area of
segment ADBCA = (Ï€(√3)^2)/2+Ï€ × 2^2 × 120/360 – 1/2 × 1 × 2√3 = 17Ï€/6- √3

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