Central Angle Theorem

The central angle theorem states that the angle subtended by a chord at the centre of a circle is exactly twice the angle subtended by the same chord at any point on the remaining part of the circumference.

The simulation draws a circle with chord AB, a movable point P on the opposite arc, and the radii OA and OB. Step buttons let students advance through the classic proof, revealing the isosceles triangles and exterior‑angle relationships. As P is dragged, the angles ∠APB and ∠AOB update in real time, confirming the 2 : 1 ratio.

By interacting with the proof steps and observing the dynamic angles, learners reinforce their understanding of circle geometry, angle relationships, and logical reasoning used in geometric proofs.