An arc of a circle of radius 21 cm subtends an angle of $60°$ at the centre. Find:
(i) the length of the arc.
(ii) the area of the minor segment of the circle made by the corresponding chord.

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Accepted Answer

Step 1: (i) Length of the arc $AB = 2 	imes \frac{22}{7} 	imes 21 	imes \frac{60}{360}$
Step 2: $= 22$ cm
Step 3: (ii) Area of sector $OALB = \frac{22}{7} 	imes 21 	imes 21 	imes \frac{60}{360} = 231$ cm$^2$
Step 4: Area of $	riangle OAB = \frac{\sqrt{3}}{4} 	imes 21 	imes 21 = \frac{441\sqrt{3}}{4}$ cm$^2$
Area of minor segment $= \left(231 - \frac{441\sqrt{3}}{4}ight)$ cm$^2$
or $(231 - 190.95) = 40.05$ cm$^2$

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