Question

Question 5 (iii)
In a circle of radius 21 cm, an arc subtends an angle of ${60}^{\circ }$ at the centre. Find:
(iii) area of the segment formed by the corresponding chord

Answer 1

(iii) Area of equilateral $\Delta AOB=\frac{\sqrt{3}}{4}\times (OA{)}^2=\frac{\sqrt{3}}{4}\times {21}^2=(441\frac{\sqrt{3}}{4})c{m}^2$
Area of the segment formed by the corresponding chord = Area of the sector formed by the arc - Area of equilateral
Area of the segment $=231c{m}^2-\left(441\frac{\sqrt{3}}{4}\right)c{m}^2$