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The Johnson midpoint is the point of concurrence of the line segments joining the vertices of a reference triangle with the centers of a certain set of circles (that resemble but are not the Johnson circles). It also is the midpoint of each of these segments, as well as perspector of the reference triangle and the triangle determined by the centers of these circles.

It has triangle center function

and is Kimberling center .

See also

Johnson Circles, Johnson's Theorem, Johnson Triangle

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References

Kimberling, C. "Encyclopedia of Triangle Centers: X(495)=Johnson Midpoint." https://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X495.

Referenced on Wolfram|Alpha

Johnson Midpoint

Cite this as:

Weisstein, Eric W. "Johnson Midpoint." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/JohnsonMidpoint.html

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