The first mid-arc point is the triangle center with triangle center function
![alpha_(177)=[cos(1/2B)+cos(1/2C)]sec(1/2A).](/https/mathworld.wolfram.com/images/equations/FirstMid-ArcPoint/NumberedEquation1.svg) |
It is Kimberling center 
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First Mid-Arc Point
See also
Mid-Arc Points, Second Mid-Arc Point, Third Mid-Arc PointExplore with Wolfram|Alpha
References
Kimberling, C. "Encyclopedia of Triangle Centers: X(177)=1st Mid-Arc Point." https://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X177.Referenced on Wolfram|Alpha
First Mid-Arc PointCite this as:
Weisstein, Eric W. "First Mid-Arc Point." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FirstMid-ArcPoint.html