Question

Chord AB of a circle subtends an angle of 120° at the centre O of the circle. Find the length of arc AB, if radius of the circle is 21 cm.

Answer 1

Given:

Radius of the circle (r) = 21 cm

Angle subtended by the arc at the centre (θ) = 120°

To find:

Length of arc AB

Calculation:

Using the formula for length of an arc:

Length of arc = `θ/(360^circ) xx 2πr`

Substituting the values:

Length of arc AB = `(120^circ)/(360^circ) xx 2 xx 22/7 xx 21`

= `1/3 xx 2 xx 22 xx 3`

= 2 × 22

= 44 cm