Circle-only constructions

Divide a centre into quarters (Chenery's method)

The problem of dividing a circle into four is popularly known as 'Napoleon's problem'. Napoleon is known to have introduced Mascheroni's compass work to French mathematicians, including Lagrange and Laplace. Study the above construction, which shows an improvement on Mascheroni's original method, created by Fitch Chenery in 1953, then see if you can do it yourself: