# On the Diagonals of a Cyclic Quadrilateral

@inproceedings{Alsina2007OnTD, title={On the Diagonals of a Cyclic Quadrilateral}, author={Claudi Alsina and Roger B. Nelsen}, year={2007} }

We present visual proofs of two lemmas that reduce the proofs of expressions for the lengths of the diagonals and the area of a cyclic quadrilateral in terms of the lengths of its sides to elementary algebra.

## 11 Citations

### A Condition for a Circumscriptible Quadrilateral to be Cyclic

- Mathematics
- 2008

We give a short proof of a characterization, given by M. Radi´ c et al, of convex quadrilaterals that admit both an incircle and a circumcircle.

### Diametric Quadrilaterals with Two Equal Sides.

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(2009). Diametric Quadrilaterals with Two Equal Sides. The College Mathematics Journal: Vol. 40, No. 1, pp. 17-21.

### HERON QUADRILATERALS VIA ELLIPTIC CURVES.

- MathematicsRocky Mountain journal of mathematics
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This work establishes a correspondence between Heron quadrilaterals and a family of elliptic curves of the form y 2 = x 3 + αx 2 - n 2 x, which generalizes the notions of Goins and Maddox and explores their connection with congruent numbers.

### On a Circle Containing the Incenters of Tangential Quadrilaterals

- Mathematics
- 2014

When we fix one side and draw different tangential quadrilaterals having the same side lengths but different angles we observe that their incen- ters lie on a circle. Based on a known formula…

### Euclidean Geometry and Elliptic Curves

- Mathematics, Computer Science
- 2020

Firstly, the important properties of these figures are investigated and then utilizing these properties, it is shown that how to construct various families of elliptic curves with different positive ranks having different torsion subgroups.

### The New Proof of Ptolemy’s Theorem & Nine Point Circle Theorem

- Mathematics
- 2016

The main purpose of the paper is to present a new proof of the two celebrated theorems: one is “Ptolemy's Theorem” which explains the relation between the sides and diagonals of a cyclic…

### 101.38 Metric relations in crossed cyclic quadrilaterals

- MathematicsThe Mathematical Gazette
- 2017

101.38 Metric relations in crossed cyclic quadrilaterals The cyclic quadrilateral is probably the quadrilateral that appears most frequently in higher Euclidean geometry problem solving. This is a…

### Diametric Quadrilaterals with Two Equal Sides

- Education
- 2009

Ray Beauregard (beau@math.uri.edu) received his B.A. from Providence College in 1964 and his Ph.D. in 1968 (under the guidance of Richard E. Johnson) from the University of New Hampshire. He has…

### ELLIPTIC CURVES ARISING FROM BRAHMAGUPTA QUADRILATERALS

- MathematicsBulletin of the Australian Mathematical Society
- 2014

Abstract A Brahmagupta quadrilateral is a cyclic quadrilateral whose sides, diagonals and area are all integer values. In this article, we characterise the notions of Brahmagupta, introduced by K. R.…

### Scavenging differential evolution algorithm for smart grid demand side management

- EngineeringProcedia Manufacturing
- 2019

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