The third mid-arc point is the triangle center with triangle center function
![alpha_(2089)=[-cos(1/2A)+cos(1/2B)+cos(1/2C)]sec(1/2A).](/images/equations/ThirdMid-ArcPoint/NumberedEquation1.svg) |
It is Kimberling center 
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Third Mid-Arc Point
See also
First Mid-Arc Point, Mid-Arc Points, Second Mid-Arc PointExplore with Wolfram|Alpha
References
Kimberling, C. "Encyclopedia of Triangle Centers: X(2089)=3rd Mid-Arc Point." http://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X2089.Referenced on Wolfram|Alpha
Third Mid-Arc PointCite this as:
Weisstein, Eric W. "Third Mid-Arc Point." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ThirdMid-ArcPoint.html