Question

The circle above with center O has a circumference of 36. What is the length of minor arc ?

*9**12**18**36*

*9**12**18**36*Hint:

### The arc of a circle consists of two points on the circle and all of the points on the circle that lie between those two points. An arc is measured not by its length (although it can be, of course) but most often by the measure of the angle whose vertex is the center of the circle and whose rays intercept the endpoints of the arc. Hence an arc can be anywhere from 0 to 360 degrees.

An arc whose measure is less than 180 degrees is called a minor arc. An arc whose measure is greater than 180 degrees is called a major arc. An arc whose measure equals 180 degrees is called a semicircle, since it divides the circle in two.

## The correct answer is: *9*

- In the question we have given the circumference of circle with centre O as 36.
- Also the arc AC which subtends the angle of 90at the centre O. So the other angle which is subtended by the arc AC will be (360°- 90°)=270°.
- So, as mentioned above the arc which subtends angle less than 180° is minor arc . So our minor arc is which subtends angle of 90° at the centre.

Θ= 90°

- Length of minor arc =

=

= 9

Therefore, the length of arc is option (A) 9

Note:- In the given question we have given the circumference, but in some questions we may have given the radius of the circle . So, instead of circumference in the formula we have to use 2πr . Where r is the radius of the circle.

Therefore, the length of arc is option (A) 9

Note:- In the given question we have given the circumference, but in some questions we may have given the radius of the circle . So, instead of circumference in the formula we have to use 2πr . Where r is the radius of the circle.

The diameter of a circle is also known as its measurement of the circle's edge, circumference, or perimeter.

As opposed to this, a circle's area indicates the space it occupies.

The circle circumference is the length when we cut it, open and draw a straight line from it.

Units like centimeters or meters are typically used to measure it.

The circle's radius is considered when applying the formula to determine the circumference of the circle.

Therefore, to calculate a circle's circumference, we must know its radius or diameter.

Therefore, the circumference of a circle formula is the circle perimeter or circumference is 2πR.

where,

R is the circle's radius.

π is a mathematical constant with an estimated value of 3.14 (to the nearest two decimal places).

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