Which theorem states that the angle at the center of a circle is twice the angle at the circumference?

The theorem that states the angle at the center of a circle is twice the angle at the circumference is known as the Angle at Center Theorem. This theorem is fundamental in circle geometry and provides a crucial understanding of the relationship between angles formed by points on a circle.

To illustrate, let’s consider a circle where you have an angle formed at the center by two radii extending to a point on the circumference. This central angle will always measure twice as much as any inscribed angle that subtends the same arc on the circle. This key relationship allows for various geometric proofs and problem-solving scenarios involving circles and angles.

Understanding this theorem is essential for solving problems related to angles in circles, as it helps establish a foundational concept that can be applied in different contexts, such as finding unknown angles, proving the properties of cyclic figures, and more.