# The theory of a convex quadrilateral and a circle that forms "Pascal points" - the properties of "Pascal points" on the sides of a convex quadrilateral

@inproceedings{Fraivert2016TheTO, title={The theory of a convex quadrilateral and a circle that forms "Pascal points" - the properties of "Pascal points" on the sides of a convex quadrilateral}, author={David Fraivert}, year={2016} }

Euclidean geometry is one of the oldest branches of mathematics – the properties of different shapes have been investigated for thousands of years. For this reason, many tend to believe that today it is almost impossible to discover new properties and new directions for research in Euclidean geometry. In the present paper, we define the concepts of “Pascal points”, “a circle that forms Pascal points”, and “a circle coordinated with the Pascal points formed by it”, and we shall prove nine… Expand

#### 6 Citations

Properties of the Tangents to a Circle that Forms Pascal Points on the Sides of a Convex Quadrilateral

- 2017

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… Expand

The Theory of an Inscribable Quadrilateral and a Circle that Forms Pascal Points

- Mathematics
- 2016

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… Expand

Properties of a Pascal Points Circle in a Quadrilateral with Perpendicular Diagonals

- 2017

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 propertie s of the Pascal points on the sides of a convex… Expand

NEW APPLICATIONS OF METHOD OF COMPLEX NUMBERS IN THE GEOMETRY OF CYCLIC QUADRILATERALS

- 2017

Any cyclic quadrilateral whose sides are not parallel can define a triangle with one vertex at the point of intersection of the quadrilateral’s diagonals and the other vertices at the points of… Expand

Pascal-points quadrilaterals inscribed in a cyclic quadrilateral

- The Mathematical Gazette
- 2019

This paper presents some new theorems about the Pascal points of a quadrilateral. We shall begin by explaining what these are. Let ABCD be a convex quadrilateral, with AC and BD intersecting at E and… Expand

Necessary and sufficient properties for a cyclic quadrilateral

- Mathematics
- International Journal of Mathematical Education in Science and Technology
- 2019

ABSTRACT There are many problems whose solution requires proof that a quadrilateral is cyclic. The main reason for writing this paper is to offer a number of new tools for proving that a particular… Expand

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