Inscribe Square in Circle using Compasses Alone/Corollary

Problem

 * To inscribe a regular dodecahedron in a given circle,
 * by means of compass alone,
 * supposing the center to be known.

Solution
We use the same construction as for Inscribe Square in Circle using Compasses Alone:


 * Inscribe-Square-in-Circle-with-Compasses.png

Then we note that, for example, $C$ and $E$ are $30 \degrees$ apart.

Hence they are adjacent vertices of a regular dodecahedron inscribed in the circle.

It remains to construct the remaining vertices, which is done by, for example, setting the compass to $CE$ and drawing an arc with center $C$ and working round the circle.