Johnson's Theorem
Let three equal Circles with centers 
, 
, and 
intersect in a single point 
and intersectpairwise in the points 
, 
, and 
. Then the Circumcircle 
of 
(the so-called JohnsonCircle) 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.
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