Demonstration of Positional Relationships among Points, Lines, and Circles

This GeoGebra applet intuitively demonstrates the positional relationships between points and circles, as well as lines and circles. By constructing circles, points, lines, and segments, and utilizing intersection commands, it dynamically displays the position of a point relative to a circle, including inside, on, or outside the circle, and the states of a line intersecting, tangent to, or disjoint from a circle. This material is suitable for middle and high school plane geometry instruction, helping students deeply understand the relative positions among geometric figures and their judgment conditions. It serves as an excellent auxiliary tool for grasping fundamental concepts in plane geometry, allowing learners to visually explore how changing parameters affects the spatial relationships between points, lines, and circles in real time.