Question

The radius of a circle is 9 cm. Find the
length of an arc of this circle which
cuts off a chord of length, equal to
length of radius.​

Answer 1

Step-by-step explanation:

Given: radius of the circle:

r = 9 cm

Since,

Length of chord = length of radius of the circle

Therefore, triangle so formed by both radii of the circle and the chord will be an equilateral triangle.

Hence, central angle

$\theta \: = 60 \degree \\ length \: of \: arc : \\ l = \frac{ \theta}{360 \degree} \times 2\pi \: r \\ = \frac{60 \degree}{360 \degree} \times 2\pi \times 9 \\ = \frac{ 1}{6} \times 18\pi \\ = 3 \pi \\ = 3 \times 3.14 \\ = 9.42 \: cm$