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

Diameter of the circle = 40 cm

∴Radius (r) of the circle = $\frac{40}{2}\,cm=20\,cm$

Let AB be a chord (length = 20 cm) of the circle.

In ΔOAB, OA = OB = Radius of circle = 20 cm

Also, AB = 20 cm

Thus, ΔOAB is an equilateral triangle.

$∴θ = 60° =\frac{\pi}{3}\,radian$

We know that in a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre, then $θ=\frac{1}{r}$

$=\frac{AB}{20}=\frac{20{\pi}}{3}\,cm$

Thus, the length of the minor arc of the chord is $\frac{20{\pi}}{3}\,cm.$