Step-by-Step Construction of an Ogee Arch Using Circle Arcs and Symmetry

This example demonstrates a step-by-step geometric construction of an ogee arch, building the arch outline by constructing circles, semicircles, and carefully selected circle arcs that meet at exactly defined points. Key math ideas include circle geometry (circles/semicircles and circle arcs), midpoint and orthogonal constructions to control curvature, intersection of lines with circles to determine construction points, and symmetry (mirroring across an axis) to obtain the full arch. In GeoGebra, the construction relies on commands such as Point (creating key points), Semicircle (initial arc foundation), Midpoint (locating the central reference), OrthogonalLine (drawing perpendicular/orthogonal guides), Segment (connecting points), Intersect (computing intersection points), Ray (directional constructs), Circle (defining circles that generate arcs), CircleArc (using arcs to form the arch boundary), and Mirror (reflecting half constructions to complete the shape). Suitable for secondary school geometry, dynamic geometry exploration, and classroom demonstrations on geometric construction techniques.