볼록사각형의 브로카르 내접 타원에 대한 연구

Abstract

This study was based on the research results conducted as a YSC project. This study expanded the study on the quadrilateral focal point of Park Kyung-soo et al. (2021) and the study on the Brocard points of quadrilaterals conducted by Frederick (1917) and Pavel et al. (2014). The results of this study are as follows. First, it was found that the focus of the inscribed ellipse of a general convex quadrilateral became the quadrilateral focal point, and the reverse was established. Second, it was found that the necessary and sufficient condition of the convex quadrilateral in which the Brocard inscribed ellipse exists is a harmonic quadrilateral. Third, the properties related to the Brocard inscribed ellipse were discovered. Fourth, the ratio of the contact between the Brocard inscribed ellipse and the quadrilateral internal division of each side was found. Fifth, the area of the Brocard inscribed ellipse was shown using the ratio. In this study, the equivalence conditions of the quadrilateral focal point found in the parallelogram was expanded to a general convex quadrilateral and various properties were discovered by expanding the Brocard inscribed ellipse defined in the triangle into a quadrilateral, and it is expected to contribute to the development of mathematics through the expansion of mathematical concepts.