# Inscribe Square in Circle using Compasses Alone/Corollary

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## Problem

*To inscribe a regular dodecagon 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:

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

Hence they are adjacent vertices of a regular dodecagon 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.

$\blacksquare$

## Sources

- 1821: John Jackson:
*Rational Amusement for Winter Evenings* - 1992: David Wells:
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