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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:
,
,
.
Then
.
You can drag the vertices
,
,
.
Contributed by:
Minh Trinh Xuan
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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
.
RELATED LINKS
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
)
PERMANENT CITATION
Minh Trinh Xuan
"
Distance between Two Napoleon Points
"
http://demonstrations.wolfram.com/DistanceBetweenTwoNapoleonPoints/
Wolfram Demonstrations Project
Published: June 15, 2022
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