Let three equal Circles with centers , , and intersect in a single point and intersect pairwise in the points , , and . Then the Circumcircle of (the so-called Johnson Circle) is congruent to the original three.

**References**

Emch, A. ``Remarks on the Foregoing Circle Theorem.'' *Amer. Math. Monthly* **23**, 162-164, 1916.

Honsberger, R. *Mathematical Gems II.*
Washington, DC: Math. Assoc. Amer., pp. 18-21, 1976.

Johnson, R. ``A Circle Theorem.'' *Amer. Math. Monthly* **23**, 161-162, 1916.

© 1996-9

1999-05-25