Constructing with Circles: Parallels, Perpendiculars, and Intersections

This GeoGebra example demonstrates how to build a circle-based configuration using parallel and perpendicular line relationships, then locate key intersection points to reveal the resulting geometric structure. It focuses on core concepts such as circle geometry, parallelism and perpendicularity (via orthogonal constructions), line intersection, and the underlying idea connected to tangent line behavior. The construction uses GeoGebra commands: Segment to create guiding segments, Circle to define the circle, OrthogonalLine to draw perpendicular/orthogonal lines, Intersect to compute intersection points, and Line to form supporting lines. The involved objects include named points (e.g., A, B, C, D and others) and the circle/lines (e.g., a circle c and line objects f, g, h, i). Suitable for middle to high school geometry lessons and for student-led exploration of classic straightedge-and-compass style reasoning.