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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 theorems that describe the properties of “Pascal points” on the sides of a convex quadrilateral. These properties concern the following subjects: ● The ratios of the distances between the Pascal points formed on a pair of opposite sides by different circles.

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