Central Angle
an angle whose vertex is the center of the circle
A central angle is an angle whose vertex is at the center of a circle and whose sides pass through two points on the circle’s circumference. In other words, the central angle is a way of measuring the extent to which the circle is ‘cut out’ by the two points.
The size of a central angle is measured in degrees, and it can range from 0 to 360 degrees. An angle of 0 degrees is simply a point, while an angle of 360 degrees is a full circle. The central angle of a circle depends on the radius of the circle and the distance between the two points on the circle’s circumference that define the angle.
Central angles are frequently used in geometry and trigonometry to solve problems involving circles. For example, if we know the radius of a circle and the measure of its central angle, we can calculate the length of the arc that the central angle cuts out of the circle’s circumference using the formula:
Arc length = (central angle / 360) x 2πr
where r is the radius of the circle and 2πr is the circumference of the circle.
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