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Johnson Triangle Circumcircle


JohnsonTriangleCircumcircle

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

 l=-(R^2sin(3A))/(2Delta),

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. https://mathworld.wolfram.com/JohnsonTriangleCircumcircle.html

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