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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

 

Options

  •  1 : 4

  • 3 : 4

  •  3 : 8

  • 1 : 2

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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`

 

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APPEARS IN

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