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arXiv · 1912.08296

Constructions in the Locus of Isogonal Conjugates in a Quadrilateral

Daniel Hu
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Abstract

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 $\mathcal C \in \mathbb R^2$. These properties allow us to present constructions involving these cubics, such as intersections and tangent lines, using straightedge and compass.

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Daniel Hu. 2019-12-17. Constructions in the Locus of Isogonal Conjugates in a Quadrilateral. https://arxiv.org/abs/1912.08296

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