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GeezerVison is showing mathworld.wolfram.com — Mid-Arc Triangle -- from Wolfram MathWorld 
Mid-Arc Triangle
The mid-arc triangle is the triangle It has trilinear vertex matrix
where The incircle is the circumcircle of the mid-arc triangle.
The following table gives the centers of the mid-arc triangle in terms of the centers of the reference triangle for Kimberling centers
See alsoAngle Bisector, Circumcircle Mid-Arc Triangle, Incircle, Mid-Arc Points, Tangential Mid-Arc TriangleExplore with Wolfram|Alpha
More things to try: ReferencesKimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.Referenced on Wolfram|AlphaMid-Arc TriangleCite this as:Weisstein, Eric W. "Mid-Arc Triangle." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Mid-ArcTriangle.html Subject classifications | |||||||||||||||||
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whose vertices consist of the intersections of
the internal ![[(y+z)^2 x^2 x^2; y^2 (x+z)^2 y^2; z^2 z^2 (x+y)^2],](/api/image?u=https%3A%2F%2Fmathworld.wolfram.com%2Fimages%2Fequations%2FMid-ArcTriangle%2FNumberedEquation1.svg)
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with 
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