Question : Two identical circles intersect so that their centres and the points at which they intersect form a square of side $2\;\mathrm{cm}$. What is the area (in$\;\mathrm{cm^2}$) of the portion common to the two circles?
Option 1: $2\pi -4$
Option 2: $4\pi -8$
Option 3: $3\pi -4$
Option 4: $\pi -2$

Question

Question : Two identical circles intersect so that their centres and the points at which they intersect form a square of side $2\;\mathrm{cm}$. What is the area (in$\;\mathrm{cm^2}$) of the portion common to the two circles?

Option 1: $2\pi -4$

Option 2: $4\pi -8$

Option 3: $3\pi -4$

Option 4: $\pi -2$

Team Careers360 · Accepted Answer

Correct Answer: $2\pi -4$

Solution :
The length of each side of the formed square is $2\;\mathrm{cm}$.
The length of the radii of the circles = $2\;\mathrm{cm}$
The area of square $=(2\;\mathrm{cm})^2 = 4\;\mathrm{cm^2}$
The area of each circle $=\pi imes 2^2 = 4\pi\;\mathrm{cm^2}$
The area of each sector of each circle $=\frac{90^\circ}{360^\circ} imes 4\pi = \pi\;\mathrm{cm^2}$
The area of the common portion $=2 imes$ The area of each sector of each circle $–$ The area of square
The area of the common portion $=\pi imes 2 - 4 = (2\pi - 4)\;\mathrm{cm^2}$
Hence, the correct answer is $2\pi - 4$.

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Question : Two identical circles intersect so that their centres and the points at which they intersect form a square of side 2cm. What is the area (incm2) of the portion common to the two circles?Option 1: 2π−4Option 2: 4π−8Option 3: 3π−4Option 4: π−2

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Question : Two identical circles intersect so that their centres and the points at which they intersect form a square of side $2 cm$ . What is the area (in ${cm}^{2}$ ) of the portion common to the two circles?
Option 1: $2 π - 4$
Option 2: $4 π - 8$
Option 3: $3 π - 4$
Option 4: $π - 2$