The Existence of Cocyclic Formed by Angle Trisectors in a Butterfly Quadrilateral and its Application in Physics

Authors

Mardani Fitra , Mashadi , Sri Gemawati

DOI:

10.29303/jppipa.v11i2.9909

Published:

2025-02-25

Issue:

Vol. 11 No. 2 (2025): February

Keywords:

Angle trisector, Butterfly quadrilateral, Cyclic quadrilateral

Research Articles

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Fitra, M., Mashadi, & Gemawati, S. (2025). The Existence of Cocyclic Formed by Angle Trisectors in a Butterfly Quadrilateral and its Application in Physics. Jurnal Penelitian Pendidikan IPA, 11(2), 49–56. https://doi.org/10.29303/jppipa.v11i2.9909

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Abstract

One of the most intriguing results related to angle trisectors in convex quadrilaterals is Morley's Theorem, which several authors have subsequently extended to non-convex quadrilaterals. Numerous studies have explored the side lengths of angle bisectors, angle trisectors, and the area ratios formed by angle trisectors in both convex and non-convex quadrilaterals. However, no research has discussed the problem of angle trisectors in butterfly quadrilaterals. Therefore, this paper aims to extend the concept of angle trisectors to butterfly quadrilaterals. Various other quadrilaterals will be formed from the construction of these angle trisectors. By employing the concept of concyclic, we will demonstrate the existence of several concyclic quadrilaterals arising from this trisector construction. Triangle angles in butterfly quadrilaterals in geometry play an important role in physics. Geometry provides a visual and mathematical language that allows us to describe, analyze, and understand various physical phenomena.

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Author Biographies

Mardani Fitra, Universitas Riau

Mashadi, Universitas Riau

Sri Gemawati, Universitas Riau

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