Circumcircle of a Triangle (Soft Construction)

① This example demonstrates how to construct the circumcircle of a triangle by dynamically tracing the center of a circle that passes through any two vertices, ultimately locating the circumcenter. ② Core mathematical concepts include the circumcircle, circumcenter, perpendicular bisectors, and the relationship between a triangle and its circumscribed circle, along with the idea of locus in geometric construction. ③ Construction details: Using GeoGebra commands such as Segment, Circle, Center, Intersect, and Polygon, the triangle ABC is built; circles through pairs of vertices are drawn, and their center loci intersect to determine the circumcenter O, after which the circumcircle is drawn. Key objects include points A, B, C, O, segments a, b, c, and auxiliary circles and intersection points. ④ Suitable for upper middle school or high school students, this example is ideal for teaching geometric construction, exploring circumcircle properties dynamically, and understanding how loci and intersections determine unique geometric objects.