Cyclocevian Conjugate


Let P=alpha:beta:gamma be a point not on a sideline of a reference triangle DeltaABC. Let A^' be the point of intersection AP intersection BC, B^'=BP intersection AC, and C^'=CP intersection AB. The circle through A^'B^'C^' meets each sideline in two (not necessarily distinct) points A^', A^(''); B^', B^(''); and C^', C^(''). Then the lines AA^(''), BB^(''), and CC^('') concur in a point X known as the cyclocevian conjugate of P. The point has triangle center function


(Kimberling 1998, p. 226).

The Gergonne point Ge is its own cyclocevian conjugate.

The following table summarized cyclocevian conjugates for some triangle centers.

See also

Cyclocevian Triangle

Explore with Wolfram|Alpha


Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.

Referenced on Wolfram|Alpha

Cyclocevian Conjugate

Cite this as:

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

Subject classifications