# How to find the measure of the intercepted arc?I have to find the measure of an intercepted arc in a circle of radius 10 cm with the given radian measure of a central angle. I have read the central...

How to find the measure of the intercepted arc?

I have to find the measure of an intercepted arc in a circle of radius 10 cm with the given radian measure of a central angle. I have read the central angle is related to the measure of its intercepted arc but the answers in the book and my answers do not match up.

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### 1 Answer

The circumference of a circle is given by 2*pi*r where r is the radius of the circle. Here the radius is 10 which gives the circumference as 20*pi.

Angles can be expressed in many units, one of which is radians. One radian is the measure of an angle such that the length of the intercepted arc is equal to the radius of the circle. This makes the length of the arc intercepted by an angle of 2*pi radians equal to the circumference of the circle.

To find the measure of the intercepted arc; when the angle is A radians, the measure of the intercepted arc is A*r.