# Inscribe Square in Circle using Compasses Alone

## Problem

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

### Corollary

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

## Solution

Let $K$ denote the circle.

Locate point $B$ on the circumference at which one of the vertices of the square is to be located.

Construct $X$, $C$, $A$ from arcs of radius of $K$ center $B$, $X$ and $C$ respectively.

Construct arcs $CD$ and $XD$ with center $B$ and $A$ respectively of radius $BC$ and $AX$ respectively.

Construct $E$ and $F$ on the circumference of $K$ so as to make $AE$ and $AF$ the same length as $OD$.

$\Box AEBF$ is the square required.

$\blacksquare$