Crosspoint

If P=p:q:r and U=u:v:w are distinct trilinear points, neither lying on a sideline of the reference triangle DeltaABC, then the crosspoint of P and U is the point

Let DeltaA^'B^'C^' be the Cevian triangle of P and DeltaA^('')B^('')C^('') the Cevian triangle of U. Let A^(''')=AA^('') intersection B^'C^', and define B^(''') and C^(''') cyclically. Then X is the perspector of triangles DeltaA^'B^'C^' and DeltaA^(''')B^(''')C^(''').

U is the X-cross conjugate of P and P is the X-cross conjugate of U.

See also

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Cite this as:

Weisstein, Eric W. "Crosspoint." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Crosspoint.html

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