The Circle Theorem refers to a set of geometric principles that describe the relationships between angles and segments in a circle. One key aspect is that the angle subtended by an arc at the center of the circle is twice the angle subtended at any point on the circumference. This means that if you draw two lines from the ends of an arc to any point on the circle, the angle formed at that point will always be half of the angle formed at the center. Another important part of the Circle Theorem is the concept of cyclic quadrilaterals. A cyclic quadrilateral is a four-sided figure where all vertices lie on the circumference of a circle. The theorem states that the opposite angles of a cyclic quadrilateral are supplementary, meaning they add up to 180 degrees. This property is useful in various geometric proofs and applications involving circles and angles.