Sándor N. Kiss and
Zoltán Kovács, Isogonal conjugacy through a fixed point
theorem,
Forum Geometricorum, 16
(2016) 171--178.
Abstract. For all point X in the plane set the affine combination of orthogonal
projections with respect to the sides of a fixed triangle, where the
coefficients are the absolute barycentric coordinates
of the point with respect to the triangle. We prove that this map is affine if
and only if X lies not on the circumcircle, and the only fixed point of this
map is the isogonal conjugate of the point X.
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