Two circles P and Q, each of radius 2 cm, pass through each other’s centres. They intersect at points A and B.

Question

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?

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Accepted Answer

17 π 6 − 3 \frac{17 \pi}{6} - \sqrt 3 6 17 π ​ − 3 ​. We know that radius of circle P is 2 cm Length of MO = 1 cm radius of circle R = AO = 2 2 − 1 2 \sqrt{\ 2^2-1^2} 2 2 − 1 2 ​ = 3 \sqrt{\ 3} 3 ​ Area of overlap between the circle R and P(shaded region) = semi circle area of R + area of segment ANBOA Area of segment ANBOA = area of sector ANBM - area