Griffiths Points

"The" Griffiths point Gr is the fixed point in Griffiths' theorem. Given four points on a circle and a line through the center of the circle, the four corresponding Griffiths points are collinear (Tabov 1995).


Let the inner and outer Soddy triangles of a reference triangle DeltaABC be denoted DeltaPQR and DeltaP^'Q^'R^', respectively. Similarly, let the tangential triangles of DeltaPQR and DeltaP^'Q^'R^' be denoted DeltaXYZ and DeltaX^'Y^'Z^', respectively. Then the inner (respectively, outer) Griffiths point Gr (respectively, Gr^') is the perspector of DeltaPQR and DeltaX^'Y^'Z^' (respectively, DeltaP^'Q^'R^' and DeltaXYZ) (Oldknow 1996). The Griffiths points lie on the Soddy line. They have triangle center functions


which are Kimberling centers X_(1373) and X_(1374), respectively.

See also

First Eppstein Point, Gergonne Point, Griffiths' Theorem, Incenter, Rigby Points, Second Eppstein Point, Soddy Line, Soddy Triangles

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Kimberling, C. "Encyclopedia of Triangle Centers: X(1st Griffiths Point)=1373.", C. "Encyclopedia of Triangle Centers: X(2nd Griffiths Point)=1374.", A. "The Euler-Gergonne-Soddy Triangle of a Triangle." Amer. Math. Monthly 103, 319-329, 1996.Tabov, J. "Four Collinear Griffiths Points." Math. Mag. 68, 61-64, 1995.

Referenced on Wolfram|Alpha

Griffiths Points

Cite this as:

Weisstein, Eric W. "Griffiths Points." From MathWorld--A Wolfram Web Resource.

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