2026 · Q53
A chord of a circle makes an angle of 90° at the centre of the circle. If the area of the major segment is k times the area of the minor segment, then what is the value of k? (Take π = 22/7)
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A8
- B9
- C10
- D11
Explanation
The minor segment is sector minus triangle: r²π/4 − r²/2 = r²(π − 2)/4. The major segment is the circle minus this: r²π − r²(π − 2)/4 = r²(3π + 2)/4. Hence k = (3π + 2)/(π − 2); with π = 22/7 this is (80/7)/(8/7) = 10, option C.