...$C$¹

This is a ``modern compass''. Originally, most construction problems were stated in terms of a ``Euclidean compass'' which collapses after each circle is drawn. In other words, a Euclidean compass cannot be used to copy a length. But it is possible to do any construction with a Euclidean compass that can be done with a modern compass. In fact, all constructions that can be done with a straight-edge and compass can be done with a compass alone--this is called the Mohr-Mascheroni Theorem.

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... footnote²

The cosine of $72^\circ$ is $(\sqrt{5}-1)/4$

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