five circles theorem

Let five circles with concyclic centers be drawn such that each intersects its neighbors in two points, with one of these intersections lying itself on the circle of centers. By joining adjacent pairs of the intersection points which do not lie on the circle of center, an (irregular) pentagram is obtained each of whose five vertices lies on one of the circles with concyclic centers. Let the circle of centers have radius r and let the five circles be centered and angular positions θ_i along this circle.

five disks problem | Miquel circles | Miquel's pentagram theorem | pentagram