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Line at Infinity

The straight line on which all Points at Infinity lie. The line at infinity is given in terms of Trilinear Coordinates by


which follows from the fact that a Real Triangle will have Positive Area, and therefore that


Instead of the three reflected segments concurring for the Isogonal Conjugate of a point $X$ on the Circumcircle of a Triangle, they become parallel (and can be considered to meet at infinity). As $X$ varies around the Circumcircle, $X^{-1}$ varies through a line called the line at infinity. Every line is Perpendicular to the line at infinity.

See also Point at Infinity

© 1996-9 Eric W. Weisstein