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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

.

Define:

,

,

.

Then

.

You can drag the vertices

,

,

.

Contributed by: Minh Trinh Xuan

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Automatic Animation

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.

Napoleon Points (Wolfram MathWorld)

The Sum of the Trilinear Coordinates of a Point (Wolfram Demonstrations Project)

Conway Triangle Notation (Wolfram Demonstrations Project)

Relating Trilinear and Tripolar Coordinates for a Triangle (Wolfram Demonstrations Project)

Brocard Angle (Wolfram MathWorld)

Minh Trinh Xuan

"Distance between Two Napoleon Points"
http://demonstrations.wolfram.com/DistanceBetweenTwoNapoleonPoints/
Wolfram Demonstrations Project
Published: June 15, 2022

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