DSE Circle: Relationship Between Angles at Centre and Circumference

This GeoGebra applet demonstrates the geometric relationship between angles at the centre and angles at the circumference of a circle. By dynamically constructing circles, points, segments, and arcs, it visually illustrates the theorem that the angle at the centre is twice the angle at the circumference subtended by the same arc. Ideal for DSE Mathematics and secondary geometry education, helping students build a deep intuitive understanding of one of the most important circle theorems. Users can manipulate points along the circle and observe in real time how the central angle and the inscribed angle change while maintaining their fixed ratio. This interactive exploration reinforces the theoretical result through hands-on discovery, allowing learners to verify the relationship across multiple configurations. The applet is particularly suited to classroom instruction and independent practice, as it guides students through observation, conjecture, and proof. Teachers can use it to introduce the theorem, prompt discussion, or assign investigative tasks where students record measurements and identify patterns. The construction is clean and uncluttered, with clearly labelled angles and arcs, ensuring that the focus remains on the mathematical relationship rather than on extraneous details. By combining dynamic geometry with the rigour expected in DSE examinations, this resource bridges the gap between visual intuition and formal geometric reasoning, making it an effective tool for both teaching and self-study.