Definition:Isogonal Conjugate

Definition

Let $X$ be a point in the plane containing a triangle $ABC$.

Let $A X_A$, $B X_B$ and $C X_C$ be the reflections of the lines $AX$, $BX$, and $CX$ about the angle bisectors at $A$, $B$, and $C$ respectively.

The isogonal conjugate of $X$ with respect to $\triangle ABC$ is the point $X^{-1}$ at which $A X_A$, $B X_B$ and $C X_C$ concur.

Also see

• Results about isogonal conjugates can be found here.

Sources

• Weisstein, Eric W. "Isogonal Conjugate." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/IsogonalConjugate.html