Central Angle vs Inscribed Angle

This interactive applet demonstrates the relationship between a central angle and an inscribed angle subtended by the same arc. By constructing a circle with a center and points on the circumference, users can drag a point to dynamically observe and verify the theorem that the central angle is always twice the inscribed angle. The applet guides students through a hands-on exploration of the Inscribed Angle Theorem, one of the most fundamental results in Euclidean geometry. A circle is drawn with its center clearly marked, and two additional points are placed on the circumference. Lines are connected to form a central angle at the circle's center and an inscribed angle sharing the same arc. As the student drags the movable point along the circle, both angles update in real time, visually reinforcing the invariant relationship between them. This dynamic approach helps learners move beyond rote memorization by allowing them to see the geometric relationship in action from multiple configurations. Students can experiment with different positions of the inscribed angle and observe that regardless of where the point is placed on the remaining arc, the measure of the central angle consistently remains exactly twice that of the inscribed angle. This repeated observation builds intuition and confidence in the theorem before a formal proof is introduced. The applet is particularly well suited for classroom instruction or independent study, as it transforms an abstract geometric property into a tangible, interactive experience. Teachers can use it to pose questions, prompt conjectures, and scaffold the transition from empirical discovery to deductive reasoning.