Autors: Nenkov, V.N., Ivanov, Y.N., Velchev, A. P., Stefanov, ST.
Title: More on the Circumscribed Quadrilateral
Keywords: circumscribed quadrilateral, incircle, Brocаrd's theorem

Abstract: In the first part of this article we consider different properties of the circumscribed quadrilaterals. Two of them concern the lines defined by the points of intersection of the incircle with the opposite /respectively adjacent/ pairs of sides of the quadrilateral. One of the considered properties of a circumscribed quadrilateral is a consequence of Brocаrd's famous theorem for inscribed quadrilateral. Another property concerns the incircles of the two triangles, defined by a diagonal of a circumscribed quadrilateral and its vertices, which do not lay on this diagonal. A recently discovered property of a circumscribed quadrilateral is also considered; it is a dependence, which involves the distances from the incenter to quadrilateral’s vertices. In the case when a quadrilateral is also inscribed, by means of this dependence is deduced another interesting relation between these distances. Also of interest is another considered property of the circumscribed quadrilateral, concerning

References

    Issue

    14th International Conference on Geometry and Applications, 2019, Bulgaria,

    Вид: пленарен доклад в международен форум