Which constructions are possible using only the circle construction tool?

In 1797 an Italian geometer, Lorenzo Mascheroni, proved that every compass-and-straight-edge construction can be done with a compass alone. For this reason such constructions are still called Mascheroni constructions.

Try these challenges. You will be constructing points and circles only - no lines. Some of the harder solutions are based on Martin Gardner's Mathematical Circus - see Sources.

Easier

Harder