 TOPICS  # 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 be denoted and , respectively. Similarly, let the tangential triangles of and be denoted and , respectively. Then the inner (respectively, outer) Griffiths point Gr (respectively, ) is the perspector of and (respectively, and ) (Oldknow 1996). The Griffiths points lie on the Soddy line. They have triangle center functions   (1)   (2)

which are Kimberling centers and , respectively.

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

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## References

Kimberling, C. "Encyclopedia of Triangle Centers: X(1st Griffiths Point)=1373." http://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X1373.Kimberling, C. "Encyclopedia of Triangle Centers: X(2nd Griffiths Point)=1374." http://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X1374.Oldknow, 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.

Griffiths Points

## Cite this as:

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