The Poncelet-Steiner theorem

The Poncelet-Steiner theorem states that if you start with a circle and a straight line that intersect inside the circle (a "diameter"), then all other geometric constructions involving just a compass and straightedge can be performed if you know just that initial line and circle. Essentially, once you have this basic setup, you can recreate any ruler-and-compass construction without directly using a ruler, confirming that the line and circle together contain all the necessary tools for classical geometry.