Distance between Two Fermat Points

Let and be the Fermat points [1] of the triangle ; is the point with minimum sum of distances to the vertices. Let be the circumradius of and be the Brocard angle [2] of .
The triangles and are the third vertices of equilateral triangles drawn on the outside and inside of .
(shown in green),
You can drag the vertices , , .


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[1] E. W. Weisstein. "Fermat Points" from Wolfram MathWorld—A Wolfram Web Resource. mathworld.wolfram.com/FermatPoints.html.
[2] E. W. Weisstein. "Brocard Angle" from Wolfram MathWorld—A Wolfram Web Resource. mathworld.wolfram.com/BrocardAngle.html.
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