In a circle of diameter 30 cm, the length of a chord is 15 cm. Find the length of the minor arc of the chord.

Answer

`15.71 cm`

Explanation

Let O be the centre of the given circle of radius 15 cm and let AB be the chord of length 15 cm. Then, `OA = OB = AB = 15 cm`.
`:. DeltaAOB ` is an equilateral triangle.
`:. DeltaAOB` is an equilateral triangle.
And therefore, `theta = angleAOB = 60^(@)`.
Let the minor arc `AB= l cm`. Then,
`theta = (pi/3)^(c )` and `r = 15` cm .
`:. theta = (l)/(r ) rArr l = rtheta = (15 xx pi/3) cm`
`= (5 xx 22/7) cm = (110)/(7) cm = 15.71 cm`