XAT 2021 Geometry & Mensuration Question (Hard)

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?

Optima Learn · Accepted Answer

Let circle P have centre at P 0,0 and radius 2. Circle Q has centre at Q 2,0 and radius 2 since each passes through the other s centre, PQ 2 . Intersection points A and B satisfy x 2 y 2 4 and x-2 2 y 2 4. Subtracting the second from the first gives x 2 - x-2 2 0 Rightarrow 4x - 4 0 Rightarrow x 1.

XAT 2021 Geometry & Mensuration — Previous Year Question

XAT 2021

Quantitative

Geometry & Mensuration

Hard

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