# Necessary and sufficient properties for a cyclic quadrilateral

```@article{Fraivert2019NecessaryAS,
title={Necessary and sufficient properties for a cyclic quadrilateral},
author={David Fraivert and Avi Sigler and Moshe Stupel},
journal={International Journal of Mathematical Education in Science and Technology},
year={2019},
volume={51},
pages={913 - 938}
}```
• Published 17 August 2020
• Mathematics
• International Journal of Mathematical Education in Science and Technology
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 quadrilateral is cyclic, thus expanding the present knowledge base and ensuring that investigators in mathematics and teachers of mathematics have at their disposal the most suitable tool available for solving the problem at hand. This present paper presents an overall summary and further development…
2 Citations

### Sequences of ratios of a convex quadrilateral

• F. Laudano
• Mathematics
International Journal of Mathematical Education in Science and Technology
• 2021
We introduce the concept of the sequence of the ratios of convex quadrilaterals, identify some properties of these sequences and use them to provide new characterizations for some classic

### NEW CHARACTERIZATIONS OF TANGENTIAL QUADRILATERALS

• Mathematics
• 2020
. We prove 13 new necessary and suﬃcient conditions for when a convex quadrilateral can have an incircle.

## References

SHOWING 1-10 OF 13 REFERENCES

### THE THEORY OF AN INSCRIBABLE QUADRILATERAL AND A CIRCLE THAT FORMS PASCAL POINTS

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

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

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

### 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

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

This book discusses Euclidean Geometry, an Elementary Treatise on the Geometry of the Triangle and the Circle and its Subgeometries, and its Applications.

### Geometrical miniature

• G. D. Gleizer (Ed.), (In Russian). Moscow: Prosveshenie.
• 1990

### Lessons in geometry: Plane geometry (Vol

• I). Providence: AmericanMathematical Society.
• 2008

• 1967