If *ABC* is an arc of a circle and ∠*ABC** *= 135°, then the ratio of arc \[\stackrel\frown{ABC}\] to the circumference is

#### Options

1 : 4

3 : 4

3 : 8

1 : 2

#### Solution

3 : 8

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

Length of the arc = `theta/(360°) 2 pi r`

Here, it is given that the arc subtends an angle of 135°with its centre. So the length of the given arc in a circle with radius ‘*r*’ is given as

Length of the arc = `(135°)/(360°) 2 pi r`

The circumference of the same circle with radius ‘*r*’ is given as `2pi r`.

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

`"Lenght of the arc"/"Cirrumference of the circle"= (135° (2 pi r))/(360° (2 pi r))`

`= (135°)/(360°)`

`=3/8`