Angle Subtended by an Arc at the Centre and at the Remaining Arc

①This GeoGebra example dynamically demonstrates the relationship between the angle subtended by an arc at the centre of a circle and the angle subtended by the remaining arc at a point on the circle, showing that their sum is 180°.②Core mathematical concepts include arcs, central angles, inscribed angles (angles subtended by an arc), and supplementary angles, fundamental properties of circles in plane geometry.③Construction details: uses the Circle command to create the circle, Point to place points A, B, C, D on the circle, Segment to draw chords and radii, Angle to measure angle α (central angle) and angle β (inscribed angle on the remaining arc), with text1 and text2 displaying the angle values; dragging points allows dynamic exploration.④Suitable for upper middle school or high school students learning circle properties, and for teachers demonstrating geometric theorems in class or for students' independent inquiry, fostering dynamic geometry thinking.