Circle Size Control: Radius-Driven Circumference and Area

This example demonstrates how changing a circle’s radius controls the overall “size” of the circle and updates related measurements such as circumference and area. It centers on key geometry concepts: radius, circumference, and area, highlighting their functional dependence on the radius through GeoGebra’s measurement outputs. Construction-wise, it uses GeoGebra commands to (1) create a circle via 『Circle』 from a center point and a radius, (2) define the needed controlling points with 『Point』, and (3) build radius-related segments using 『Segment』 so the radius object (e.g., r/Radius) stays linked to the geometry. The circle’s 『Circumference』 and 『Area』 are then displayed as dynamically updated objects. Suitable for middle and high school geometry lessons and for introducing parameter-driven visualization of geometric quantities.