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ircle only constructions Here is a menu of all the pages available: --- Select --- Foundation Intermediate Advanced ---------------- Euclid sacred geometry Circle-only constructions Transformations Hidden world of... Classic problems ---------------- Introduction Thinking A brief history... Sources Tech Buttons Tutors Click on the above picture to return here. Which constructions are possible using only the circle construction tool? In 1797 an Italian geometer, Lorenzo Mascheroni, proved that every compass-and-straightedge 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 Construct a symmetric point Construct the equilateral triangle ABC Construct a perpendicular Construct the 60° rhombus Double the length AB Construct a regular hexagon Construct the midpoint of AB Construct the square ABCD Construct a square given diagonal corners Construct the bisector of an arc Construct a ratio Construct the circumcircle of ABC Construct the centre of a circle Divide a circle into quarters Construct a regular pentagon