2019 · Q75
Considering two opposite vertices of a square of side ‘a’ as centres, two circular arcs are drawn within the square joining the other two vertices, thus forming two sectors. What is the common area in these two sectors?
Elementary MathematicsCircles
- Aa²(π + 1/2)
- Ba²(π - 1/2)
- Ca²(π/2 - 1)
- Da²(π/2 + 1)
Explanation
Each arc is a 90-degree sector of radius a, with area pi*a^2/4. The lens-shaped overlap of the two sectors equals the sum of the two sector areas minus the square (which is covered twice): 2*(pi*a^2/4) - a^2 = a^2*(pi/2 - 1). Hence the common area is a^2*(pi/2 - 1), option (c).