Weill Point

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


For a triangle DeltaABC, the Weill point W is the triangle centroid of the contact triangle DeltaA^'B^'C^'. The Weill point is Kimberling center X_(354), and has equivalent triangle center functions


If O, I and W are the circumcenter, incenter, and Weill point of a triangle DeltaABC, then W lies on the line OI and


where r and R are the inradius and circumradius of DeltaABC.

See also

Weill's Theorem

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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.

Referenced on Wolfram|Alpha

Weill Point

Cite this as:

Weisstein, Eric W. "Weill Point." From MathWorld--A Wolfram Web Resource.

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