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Orthoptic Circle of the Steiner Inellipse


OrthopticCircleOfTheSteinerInellipse

The orthoptic circle of the Steiner inellipse is the circle with center at

 alpha_2=1/a,
(1)

corresponding to the triangle centroid G and radius

 r=(sqrt(a^2+b^2+c^2))/(3sqrt(2)).
(2)

It has circle function

 l=-1/3cosA,
(3)

corresponding to the circumcenter O=X_3.

It does not pass through any Kimberling centers.

OrthopticCircleoftheSteinerInellipseOrthogonal

It is orthogonal to the Parry circle (green) and Stevanović circle (blue).


See also

Steiner Inellipse

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Cite this as:

Weisstein, Eric W. "Orthoptic Circle of the Steiner Inellipse." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/OrthopticCircleoftheSteinerInellipse.html

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