Circles and a Rectangle: Radius Problem with Area 243

① This example demonstrates a classic geometry puzzle: a rectangle containing two tangent circles and a semicircle, with the small circle radius given as 6 cm and the total area as 243 cm², challenging the solver to find the large circle's radius or other dimensions. ② Core mathematical concepts include area of circles and rectangles, similar triangles, rotational symmetry, and optimization; equations are derived from geometric relationships to solve for unknowns. ③ Construction highlights: from the summary, GeoGebra commands such as Point, Mirror, Parabola, Circle, Polygon, Segment, Intersect, and Distance are used, creating circles, polygons, segments, intersection points, and distance measurements, with buttons and dropdown lists for interactive exploration. ④ Suitable for high school or early college students to train geometric intuition, algebraic modeling, and problem-solving skills, and also as an engaging classroom demonstration for teachers.