Distance between Two Fermat Points

Let and be the Fermat points [1] of the triangle ; is the point with minimum sum of distances to the vertices. Let be the circumradius of and be the Brocard angle [2] of .
The triangles and are the third vertices of equilateral triangles drawn on the outside and inside of .
Define:
(shown in green),
,
.
Then
.
You can drag the vertices , , .

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

References
[1] E. W. Weisstein. "Fermat Points" from Wolfram MathWorld—A Wolfram Web Resource. mathworld.wolfram.com/FermatPoints.html.
[2] E. W. Weisstein. "Brocard Angle" from Wolfram MathWorld—A Wolfram Web Resource. mathworld.wolfram.com/BrocardAngle.html.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.