The half-Moses circle is defined as the circle having the same center as the Moses circle, i.e., the Brocard midpoint 
but half its radius, i.e.,
where 
is the circumradius of the reference
triangle and 
is the Brocard angle.
It has circle function
 |
(3)
|
which does not correspond to any Kimberling center.
It passes through Kimberling center 
.
See also
Moses Circle
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References
Kimberling, C. "Encyclopedia of Triangle Centers: X(1575)=Exsimilicenter of Spieker and (1/2)-Moses Circles." http://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X1575.Referenced
on Wolfram|Alpha
Half-Moses Circle
Cite this as:
Weisstein, Eric W. "Half-Moses Circle."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Half-MosesCircle.html
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