Question

If ABC is an arc of a circle and ∠ABC = 135°, then the ratio of arc $\stackrel{⏜}{ABC}$ to the circumference is

(a) 1 : 4

(b) 3 : 4

(c) 3 : 8

(d) 1 : 2

Answer 1

(c) 3 : 8

The length of an arc subtending an angle ‘’ in a circle of radius ‘r’ is given by the formula,

Length of the arc =

Here, it is given that the arc subtends an angle of with its centre. So the length of the given arc in a circle with radius ‘r’ is given as

Length of the arc =

The circumference of the same circle with radius ‘r’ is given as .

The ratio between the lengths of the arc and the circumference of the circle will be,

Hence, the correct answer is option (c).