It is obvious that if the points _P′_, _Q′_, _R_, etc., by which the
circle is divided in Fig. 32., be joined by right lines, the resulting
figure will be a regular equilateral figure of twenty sides inscribed
in the circle. And if the circle be divided into given unequal parts,
and the points of division joined by right lines, the resulting figure
will be an irregular polygon inscribed in the circle with sides of
given length.
Thus any polygon, regular or irregular, inscribed in a circle, may be
inscribed in position in a perspective circle.