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Journal for Geometry and Graphics 27 (2023), No. 2, 127--149
Copyright Heldermann Verlag 2023

The Quadrilateral Coordinated with a Circle that Forms Pascal Points and its Properties

David Fraivert
Shaanan College, Haifa, Israel

In the present paper, the concept of "a quadrilateral coordinated with a circle that forms Pascal points" ("coordinated quadrilateral" for short) is defined as a quadrilateral for which there exists a circle that forms Pascal points on the sides of the quadrilateral, and for which it holds that the following four points are collinear: the point of intersection of the extensions of the two opposite sides of the quadrilateral, the center of the circle, and the two Pascal points formed by it.
We investigate and prove the properties of this quadrilateral. These properties may be divided into two sets: (i) properties of the straight lines, line segments, and angles associated with the coordinated quadrilateral and (ii) properties of the circles associated with the coordinated quadrilateral. In addition, we show a method for constructing the coordinated quadrilateral.

Keywords: Coordinated quadrilateral, circle that forms Pascal points, collinearity of points, geometric construction.

MSC: 51M04; 51M05, 51M15, 51N20.

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