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# Weill Point

Weill's theorem states that, given the incircle and circumcircle of a bicentric polygon of sides, the centroid of the tangent points on the incircle is a fixed point , known as the Weill point, independent of the orientation of the polygon.

For a triangle , the Weill point is the triangle centroid of the contact triangle . The Weill point is Kimberling center , and has equivalent triangle center functions

 (1) (2)

If , and are the circumcenter, incenter, and Weill point of a triangle , then lies on the line and

 (3)

where and are the inradius and circumradius of .

Weill's Theorem

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## References

Gallatly, W. "The Weill Point." §238in The Modern Geometry of the Triangle, 2nd ed. London: Hodgson, p. 19, 1913.M'Clelland, W. J. A Treatise on the Geometry of the Circle and Some Extensions to Conic Sections by the Method of Reciprocation, with Numerous Examples. London: Macmillan, p. 96, 1891.Weill. Liouville's J. (Ser. 3) 4, 270, 1878.

Weill Point

## Cite this as:

Weisstein, Eric W. "Weill Point." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/WeillPoint.html