Fixed Compass drawing Smaller Circle

Problem

How can a rusty compass be used to draw a circle whose radius is smaller than that of the compass opening?

Solution 1

The circle is drawn on the surface of a sphere.

$\blacksquare$

Solution 2

The point of the compass is placed at the apex of a right circular cone, and the circle is drawn on its surface.

$\blacksquare$

Historical Note

This puzzle is typical of those found in collections of Victorian amusements.

Sources

• 1633: Henry van Etten: Mathematicall Recreations (translated by William Oughtred from Récréations Mathématiques)
• 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): Henry van Etten: $120$