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
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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.
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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
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Diametric Quadrilaterals with Two Equal Sides
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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…
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