Catriona’s Semicircles Construction Puzzle

This example demonstrates how arranging multiple semicircles and their intersection relationships can reveal geometric constraints driven by tangency and symmetry. The key concepts include circle and semicircle geometry, tangent (tangency) conditions, mirror symmetry (reflection as a transformation), and using intersection points to determine critical locations. Construction is reflected in the GeoGebra command set: Point is used to create the essential points (A, B, c, C, C′, d, D, f, i, E, E′, e), Circle provides the underlying circles for the semicircles, Mirror generates symmetric counterparts such as C′ and E′, Semicircle constructs the semicircular arcs, Intersect finds the necessary intersection points to lock the configuration, and Line draws the connecting/auxiliary lines (including tangent candidates) that complete the puzzle. Suitable for middle-school to early high-school geometry lessons, construction-based problem solving, and contest-style exploration.