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Garfunkel's Inequality


GarfunkelsInequality

Let I be the incenter of a triangle DeltaABC and U, V, and W be the intersections of the segments IA, IB, IC with the incircle. Also let the centroid G lie inside the incircle and D, E, and F be the intersections of the segments GA, GB, GC with the incircle. Then the perimeter of DeltaUVW is less than or equal to that of DeltaDEF, as proposed by Garfunkel (1981, 1982) and proved by Nyugen and Dergiades (2004).


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References

Garfunkel, J. "Problem 648." Crux Math. 7, 178, 1981.Garfunkel, J. "Solution to Problem 648." Crux Math. 8, 180-182, 1982.Nyugen, M. H. and Dergiades, N. "Garfunkel's Inequality." Forum Geom. 4, 153-156, 2004. http://forumgeom.fau.edu/FG2004volume4/FG200419index.html.

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Garfunkel's Inequality

Cite this as:

Weisstein, Eric W. "Garfunkel's Inequality." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GarfunkelsInequality.html

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