2022 · Q74
What is the area of the minor segment?
Elementary MathematicsCircles
- Al²2≤ft(π -1/2)
- Bl²4≤ft(π -1/2)
- Cl²4≤ft(π /2-1)
- Dl²2≤ft(π /2-1/2)
Explanation
Reading this item in the standard way (a square of side l inscribed in a circle, so the radius is l/√2 and each side subtends 90° at the centre): minor segment = sector − triangle = π(l/√2)²/4 − (l/√2)²/2 = πl²/8 − l²/4 = (l²/4)(π/2−1). As a consistency check, minor + major segment equals the full circle πl²/2. The keyed option is C.