Question

Question 5 (i)
In a circle of radius 21 cm, an arc subtends an angle of ${60}^{\circ }$ at the centre. Find:
(i) the length of the arc

Answer 1

Radius of the circle = 21 cm
$\left(i\right)\Delta AOB$ is isosceles as two sides are equal.
$\therefore \angle A=\angle B$
Sum of all angles of triangle = ${180}^{\circ }$
$\angle A+\angle B+\angle O={180}^{\circ }$
$\Rightarrow 2\angle A={180}^{\circ }-{60}^{\circ }$
$\Rightarrow \angle A=\frac{{120}^{\circ }}{2}$
$\Rightarrow \angle A={60}^{\circ }$
Triangle is equilateral as $\angle A=\angle B=\angle O={60}^{\circ }$

Length of arc AB = $\frac{{60}^{\circ }}{{360}^{\circ }}\times 2\times \frac{22}{7}\times 21$
The length of the arc is 22 cm.