Question

In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.

Answer 1

Let ‘O’ be the centre of the circle and AB be the chord of the circle.

Here, d = 40 cm

∴ r = ${\displaystyle \frac{40}{2}}$ = 20cm

Since OA = OB = AB,

ΔOAB is an equilateral triangle.

∴ The angle subtended at the centre by the minor

arc AOB is θ = 60° = ${\displaystyle {(60\times \frac{\pi }{180})}^{\text{c}}}$

= ${\displaystyle {\left(\frac{\pi }{3}\right)}^{\text{c}}}$

∴ ${\displaystyle l}$ (minor arc of chord AB) = rθ

= ${\displaystyle 20\times \frac{\pi }{3}}$

= ${\displaystyle \frac{20\pi }{3}\text{cm}}$