Alternative Proof of the Butterfly Theorem on a Hyperbola

M. Teguh; Mashadi Mashadi

doi:10.24198/jmi.v22.n1.70222.73-82

Alternative Proof of the Butterfly Theorem on a Hyperbola

M. Teguh, Mashadi Mashadi

Abstract

The Butterfly Theorem originally applies to a circle. Several researchers have proven the Butterfly Theorem using various methods of proof. Furthermore, the theorem has been extended from its original application on circles to other conic sections, namely the parabola and the ellipse, also through different proof techniques. In addition, the development of the Butterfly Theorem can be applied to another conic section, the hyperbola, through an analytic approach. In this paper, the author proves the Butterfly Theorem on a hyperbola using Haruki’s Lemma. Haruki’s Lemma was originally established for circles. Therefore, the author develops Haruki’s Lemma specifically for the hyperbola, which is then used to prove the Butterfly Theorem on a hyperbola. Thus, a new proof of the Butterfly Theorem on a hyperbola can be established

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DOI: https://doi.org/10.24198/jmi.v22.n1.70222.73-82