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Nobbs Points


NobbsPoints

Given a triangle DeltaABC, construct the contact triangle DeltaDEF. Then the Nobbs points are the intersections of the corresponding sides of triangles DeltaABC and DeltaDEF, i.e., the first Nobbs point D^' is the intersection of EF and BC, and similarly for E^' and F^'. The Nobbs points are collinear and fall along the Gergonne line. They have trilinear coordinates -(a-b+c)b:(-a+b+c)a:0, 0:-(a+b-c)c:(a-b+c)c, and (a+b-c)c:0:-a(-a+b+c).

Given the tangent circles of a reference triangle, the pairwise external centers of similitude are the Nobbs points.


See also

Collinear, Contact Triangle, Evans Point, Fletcher Point, Gergonne Line, Perspective Triangles

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References

Oldknow, A. "The Euler-Gergonne-Soddy Triangle of a Triangle." Amer. Math. Monthly 103, 319-329, 1996.

Referenced on Wolfram|Alpha

Nobbs Points

Cite this as:

Weisstein, Eric W. "Nobbs Points." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NobbsPoints.html

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