Constructions in the Locus of Isogonal Conjugates in a Quadrilateral

الأصل · EN

Given fixed distinct points A, B, C, D, we examine properties of the locus of points X for which (XA, XC), (XB, XD) are isogonal. This locus is a cubic curve circumscribing ABCD. We characterize all possible such cubics C ∈ R². These properties allow us to present constructions involving these cubics, such as intersections and tangent lines, using straightedge and compass.