Common Notion 3: Circle through Three Points with Tangents and Reflections

This GeoGebra example demonstrates the construction of a circle passing through three non-collinear points, along with tangent lines, perpendiculars, and reflections, to visually verify the classical geometric axiom that exactly one circle passes through any three non-collinear points. Core mathematical concepts include the uniqueness of a circumcircle, tangent line properties, reflection transformations, and the interplay of polygons and function graphs. The construction uses commands such as Point, Segment, Polygon, OrthogonalLine, Intersect, and PointIn, with objects including points A, B, C, polygon poly1, lines g, h, i, j, circles q1 and q2, tangents a_1 and f_1, and text labels Textq1. Suitable for high school geometry or introductory college geometry courses, this example helps students understand circle determination and geometric construction techniques.