The Five Circles Theorem

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Image: Wikimedia Commons

If the centers of five circles lie along the circumference of a sixth so that they overlap like the links of a chain, and if each intersects its neighbor on the sixth circle as well, then drawing lines as shown through the remaining intersections will form a pentagram whose points lie on the five circles.

A 19th-century schoolchild defined a circle as “a round straight line with a hole in the middle.”