2022 · Q75
What is the area of the major segment?
Elementary MathematicsCircles
- Al²4≤ft(3π /2+1)
- Bl²4≤ft(3π /2-1)
- Cl²2≤ft(3π /2+1)
- Dl²2≤ft(3π /2-1)
Explanation
Major segment = whole circle − minor segment = πl²/2 − (l²/4)(π/2−1) = (l²/4)(3π/2+1). Equivalently, major = three 90° sectors plus the triangle: 3πl²/8 + l²/4. The keyed option is A.