Distance between Two Napoleon Points

Let and be the outer and inner Napoleon triangles of the triangle . Let and be the two Napoleon points [1] of . Let be the circumradius of and be the Brocard angle [2] of .
Define:
,
,
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Then
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You can drag the vertices , , .

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