Intersecting Circles and Limits: How Shrinking Radius Affects Intersection Point

This interactive GeoGebra activity demonstrates how the intersection point between a variable circle and a fixed circle changes as the variable circle's radius decreases, eventually approaching a limiting position. It visually connects geometric intersection with the concept of limits in calculus. Core mathematical concepts include circle equations, solving systems of two circles, parametric variation, and limit behavior. The construction uses a button (button1) to trigger animation, an index (index) to cycle through radius values, and multiple text objects (text1 through text9) to display live coordinates, radius values, and limit hints. This resource is ideal for high school or introductory college students studying analytic geometry and pre-calculus, helping them grasp the geometric interpretation of limits and dynamic convergence.