About a given pentagon, which is equilateral and equiangular, to circumscribe a circle.
Proof
Take the same point F as in IV.13 (intersection of two
angle-bisectors). Join F to each vertex; by I.4 the resulting
triangles are congruent (equal sides, common bisected angles), so the
five distances from F to the vertices are equal. Draw the circle
on F with that radius (Definition I.15).