Semicircular Arches (Arcos de Medio Punto) Construction

This GeoGebra example demonstrates the geometric construction of semicircular arches (Arcos de Medio Punto), building a symmetric arch structure through points, segments, circles, arcs, and transformations such as reflection and rotation. The core mathematical concepts involve properties of circles and arcs, midpoints and perpendicular relationships, symmetry transformations (mirror and rotate), and vector translation in construction. The construction uses GeoGebra commands including Segment, Midpoint, Circle, Line, Intersect, If, Rotate, CircumcircleArc, Mirror, Vector, and Translate, with objects like points (A, B, C, D, E, F, K, L), arcs (c, c1, f), and auxiliary lines (g, h, i, j). This example is suitable for middle or high school geometry classes to understand circles, symmetry, and combined use of basic construction tools, and can also serve as a mathematical model for arch designs in architecture or art.