Question

If an are subtends an angle of 90° at the centre of a circle, then the ratio of its length to the circumference of the circle is ______.

Options

• 2 : 3

• 1 : 4

• 4 : 1

• 1 : 3

Answer 1

If an are subtends an angle of 90° at the centre of a circle, then the ratio of its length to the circumference of the circle is 1 : 4.

Explanation:

An arc that subtends an angle of 90° at the center of a circle represents a quarter of the full circle because a full circle has 360°

`= (90°)/(360°) = 1/4`

Therefore, the ratio of the arc length to the circumference of the circle is 1 : 4