What is a central angle and what is the relationship of the central angle and the intercepted arc?

Question

anonymous · Answer

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wolf1728 · Answer

The dictionary definition of a central angle is an angle formed at the center of a circle by two radii.
If we think of the central angle being 360° then the intercepted arc is the circle's circumference.  From this, we can determine the intercepted arc for any central angle.

anonymous · Answer

Central Angle (CA): the angle formed from the center point of the circle to each end of the Intercepted Arc (IA)

CA = IA

anonymous · Answer

As an example, for a CA of 60 degrees, the IA is 60 degrees.

wolf1728 · Answer

When the central angle is 360°, then the intercepted arc is 2*PI*radius.
If the central angle is 90° the intercepted arc is (2*PI*radius)/4
Can you determine a formula from that?