About a given circle to circumscribe an equilateral and equiangular pentagon.
Proof
Inscribe a regular pentagon in the given circle by IV.11. At each
vertex draw the tangent (III.16); the five tangents bound the
circumscribed pentagon. Each tangent is perpendicular to its radius
(III.18), and by I.4 the right triangles formed at adjacent vertices
are congruent, so the circumscribed pentagon has equal sides and
equal angles.