Let P=p:q:r and U=u:v:w be distinct trilinear points, neither lying on a sideline of DeltaABC. Then the crossdifference of P and U is the point X defined by trilinears


Treating P and U as vectors, the crossdifference is then simply given by PxU.

It can be constructed as the isogonal conjugate of the trilinear pole of the line PU. Thus, U is the crossdifference of P and X, and P is the crossdifference of U and X.

See also

Crosssum, Crosspoint

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Cite this as:

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

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