# If Abc is an Arc of a Circle and ∠Abc = 135°, Then the Ratio of Arc ⌢ a B C to the Circumference is - Mathematics

MCQ

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

•  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

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 15 Circles
Q 14 | Page 110