Circle Through Three Given Points

This example demonstrates the classic geometric construction of a unique circle passing through three given non-collinear points. It illustrates the fundamental theorem that three non-collinear points determine a circle, and highlights the role of perpendicular bisectors in locating the circle's center. The construction uses GeoGebra commands: Point to create three points A, B, C; Segment to form triangle ABC; LineBisector to construct perpendicular bisectors of AB and BC; Intersect to find their intersection D, which is the circumcenter; and Circle to draw the circle centered at D with radius DA. This activity is suitable for middle school and high school students learning geometric constructions and circle properties, and serves as an effective visual aid for teachers explaining the uniqueness of the circumcircle.