Johnson Triangle Circumcircle


The circumcircle of the Johnson triangle DeltaJ_AJ_BJ_C has center at the orthocenter H of the reference triangle and radius R, where R is the circumradius of the reference triangle. It is therefore congruent both to the circumcircle of DeltaABC and to the Johnson circles.

It has circle function


where Delta is the area of the reference triangle.

It passes through Kimberling center X_(265), which is the reflection of the circumcenter X_3 in the Jerabek center X_(125).

See also

Johnson Circles, Johnson Circumconic, Johnson's Theorem, Johnson Triangle

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Cite this as:

Weisstein, Eric W. "Johnson Triangle Circumcircle." From MathWorld--A Wolfram Web Resource.

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