The isogonal conjugate X^(-1) of a point X in the plane of the triangle Δ A B C is constructed by reflecting the lines A X, B X, and C X about the angle bisectors at A, B, and C. The three reflected lines then concur at the isogonal conjugate. In older literature, isogonal conjugate points are also known as counter points, Gegenpunkte, and focal pairs. The trilinear coordinates of the isogonal conjugate of the point with coordinates α:β:γ are α^(-1) :β^(-1) :γ^(-1).
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