# Distance between Two Vecten Points

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Let [1] and [2] be the inner and outer Vecten points [3] of the triangle . The Vecten points are based on squares constructed on each side of a triangle. Here, 45° isosceles right triangles on each side are shown. Let be the circumradius of and be the Brocard angle [2] of .

[more]

Define:

,

,

.

Then

.

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Contributed by: Minh Trinh Xuan (August 2022)
Open content licensed under CC BY-NC-SA

## Details

From the above formula we have:

.

References

[1] C. Kimberling. "X(485) = Vecten Point," Encyclopedia of Triangle Centers - ETC. (Jun 6, 2022) faculty.evansville.edu/ck6/encyclopedia/ETC.html#X485.

[2] C. Kimberling. "X(486) = Inner Vecten Point," Encyclopedia of Triangle Centers - ETC. (Jun 6, 2022) faculty.evansville.edu/ck6/encyclopedia/ETC.html#X486.

[3] E. W. Weisstein. "Vecten Points" from Wolfram MathWorld—A Wolfram Web Resource. mathworld.wolfram.com/VectenPoints.html (Wolfram MathWorld).

[4] E. W. Weisstein. "Brocard Angle" from Wolfram MathWorld—A Wolfram Web Resource. mathworld.wolfram.com/BrocardAngle.html (Wolfram MathWorld).

[5] M. T. Xuan. "Conway Triangle Notation" from the Wolfram Demonstrations Project—A Wolfram Web Resource. demonstrations.wolfram.com/ConwayTriangleNotation.

## Permanent Citation

Minh Trinh Xuan

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