Classical Construction of Pascal’s Limaçon and Cardioid as a Locus

This example demonstrates how Pascal’s limaçon and the cardioid arise as the locus of a moving point via a classical geometric construction. It highlights the idea of generating a curve from constrained motion: the locus is determined using circle geometry with tangency and orthogonality conditions. Key concepts include locus (locus of a point), tangent lines to circles, constructing perpendicular lines, and locating points through intersections. In GeoGebra, the construction uses Circle to define the base and auxiliary circles, Point to place essential defining points, Tangent to create the tangent line, OrthogonalLine to enforce the perpendicular constraint, and Intersect to compute the resulting key point that traces the curve; Segment is used to reveal the constructed geometry. The setup is intended for secondary-level advanced learning, contest preparation, and early university geometry courses focusing on construction methods and locus concepts.