Central Angle
An angle whose vertex is the center of a circle
In geometry, a central angle is an angle whose vertex is at the center of a circle and whose sides pass through any two points on the circumference of the circle. Central angles are named after the center of the circle and are measured in degrees or radians.
The measure of a central angle is equal to the measure of the arc it intercepts on the circumference of the circle. This is known as the arc degree measure relationship. So, if an angle intercepts an arc of 60° on the circumference, the central angle will also have a measure of 60°.
Central angles are important in geometry because they help us understand relationships between lengths and angles in circles. They are often used to calculate arc lengths, segment lengths, and other properties of a circle.
Examples of central angles include the angles formed by the hands of a clock, the angle formed by two radii of a circle, and the angle formed by the intersection of the tangent and the radius at a point on the circle.
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