Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: David Fraivert
Pages: [81] - [107]
Received Date: November 27, 2016
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100121742
The theory of a convex quadrilateral and a circle that forms Pascal
points is a new topic in Euclidean geometry. The theory deals with the
properties of the Pascal points on the sides of a convex
quadrilateral, the properties of “circles that form Pascal
points”, and the special properties of “the circle coordinated
with the Pascal points formed by it”.
In the present paper, we shall continue developing the theory and
expand it to the case where the quadrilateral is inscribable. We prove
five new theorems that describe properties in the following
subjects:
● Necessary and sufficient conditions for a quadrilateral to be
inscribable, which are determined by a circle coordinated with the
Pascal points formed by it.
● Properties of the perimeters and areas of quadrilaterals inscribed
in an inscribable quadrilateral, and that are associated to circles
“that form Pascal points on the sides of the quadrilateral”.
inscribable quadrilateral, tests for the inscribability of a quadrilateral, the method of complex numbers in plane geometry, Pascal points on the sides of a quadrilateral, a circle that forms Pascal points, a circle coordinated with the Pascal points formed by it, Thales’ tehorem.
