Inscribed Angle and Tangent-Chord Angle

This GeoGebra applet demonstrates the inscribed angle and tangent-chord angle theorems in circle geometry. By constructing a circle, chords, tangents, and related rays and perpendicular lines, it visually illustrates the relationship between an inscribed angle and a tangent-chord angle that subtend the same arc. Users can drag points dynamically to observe how the angles change in real time, reinforcing their understanding of the geometric properties involved. The applet allows learners to verify the key theorem that a tangent-chord angle is equal to the inscribed angle subtended by the intercepted arc. This interactive exploration supports inquiry-based learning in plane geometry, helping students move beyond memorization to genuine conceptual understanding. The dynamic construction makes it easy to test multiple configurations and see that the relationship holds universally, regardless of the positions of the points on the circle. The applet is designed for classroom instruction, self-study, and geometric investigation, providing an intuitive visual foundation for one of the most important theorems in Euclidean geometry. Teachers can use it to guide discussions, pose challenges, and encourage students to formulate and test conjectures about angle relationships in circles.