Cross Conjugate

Let P=p:q:r and U=u:v:w be distinct points, neither lying on a side line of the reference triangle DeltaABC. Then the P-cross conjugate of U is the point


Let DeltaA^'B^'C^' be the Cevian triangle of U, let A^('') be the intersection of lines PA^' and B^'C^', and define B^('') and C^('') cyclically so that DeltaA^('')B^('')C^('') is the Cevian triangle in DeltaA^'B^'C^' of P. Then the perspector of triangles DeltaABC and DeltaA^('')B^('')C^('') is the P-cross conjugate of U.

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Cite this as:

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

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