Johnson's Theorem

Let three equal Circles with centers $C_1$, $C_2$, and $C_3$ intersect in a single point $O$ and intersect pairwise in the points $P$, $Q$, and $R$. Then the Circumcircle $J$ of $\Delta PQR$ (the so-called Johnson Circle) is congruent to the original three.

See also Circumcircle, Johnson Circle

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.