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: Curious and Interesting Puzzles ... (previous) ... (next): Rational Amusements for Winter Evenings: $158$