In a given circle to inscribe an equilateral and equiangular pentagon.
Proof
Construct the 72–72–36 isosceles triangle FGH by IV.10. Inscribe
in the given circle a triangle ACD equiangular with FGH (IV.2).
Bisect the base-angles of ACD by IV.10's construction propagated
into the circle, yielding two more division points B, E. The
five arcs are equal (III.26), so the five chords AB, BC, CD,
DE, EA are equal (III.29), and the inscribed angles standing on
equal arcs are equal (III.27): the pentagon is regular.