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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 .

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Define:

,

,

.

Then

.

You can drag the vertices , , .

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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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