Distance between Two Napoleon Points

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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
.
Contributed by: Minh Trinh Xuan (August 2022)
Open content licensed under CC BY-NC-SA
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References
[1] E. W. Weisstein. "Napoleon Points" from Wolfram MathWorld—A Wolfram Web Resource. mathworld.wolfram.com/NapoleonPoints.html (Wolfram MathWorld).
[2] E. W. Weisstein. "Brocard Angle" from Wolfram MathWorld—A Wolfram Web Resource. mathworld.wolfram.com/BrocardAngle.html (Wolfram MathWorld).
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