2020 · Q92
In the given figure, what is the area of the shaded region?
Elementary MathematicsCircles
- A9(π − √3) sq units
- B3(4π − 3√3) sq units
- C3(3π − 4√3) sq units
- D9(√3 − π) sq units
Explanation
Chord 6√3 in a circle of radius 6 subtends 2·arcsin(3√3/6) = 120° at the centre. Segment area = sector − triangle = 12π − 9√3 = 3(4π − 3√3). The triangle formed by the two radii and the chord has area 9√3.