References

OPTIMIZATION OF CERTAIN COMPONENTS OF QUADRILATERALS: A SIMPLIFIED APPROACH TO OLD AND NEW PROBLEMS


[1] T. Andreescu, O. Mushkarov and L. Stoyanov, Geometric Problems on Maxima and Minima, Birkhauser, Boston, Inc., Boston, MA, 2006. ISBN: 978-0-8176-3517-6.

[2] I. B. Thomas, Selections Illustrating the History of Greek Mathematics, Vol. I, Forgotten Books, February 8, 2018. ISBN-13: 978-0656101535.

[3] I. B. Thomas, Selections Illustrating the History of Greek Mathematics, Vol. II, Forgotten Books, July 25, 2017. ISBN-13: 978-0282549244.

[4] R. A. Johnson, Advanced Euclidean Geometry, Dover Publication, 2007. ISBN-13:978-0486462370.

[5] A. Hess, A highway from Heron to Brahmagupta, Forum Geometricorum 12 (2012), 191-192. MR2955633.

[6] R. Mogilevsky and M. Stupel, Using the wonder of inequalities between averages for mathematics problems solving, Educational Research and Reviews 11(9) (2016), 932-944.
DOI: https://doi.org/10.5897/ERR2016.2763

[7] J. Haantjes, Ptolemy’s theorem, Simon Stevin 29 (1952), 25-31. MR0048827.

[8] R. Askey, Completing Brahmagupta’s Extension of Ptolemy’s Theorem, The Legacy of Alladi Ramakrishnan in the Mathematical Sciences, Springer, New York, 2010, pp. 191-197. ISBN-13: 978-1441962621.
DOI: https://doi.org/10.1007/978-1-4419-6263-8_11

[9] J. P. Pinasco, New proofs of Euclid’s and Euler’s theorems, American Mathematical Monthly 116(2) (2009), 172-174. MR2478061.

[10] L. Collins and T. J. Osler, Law of cosines generalized for any polygon and any polyhedron, The Mathematical Gazette 95(533) (2011), 240-243.
DOI: https://doi.org/10.1017/S0025557200002953