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Extensions of Vittas’ Theorem

Published online by Cambridge University Press:  15 February 2024

Nikolaos Dergiades  and
Quang Hung Tran
Nikolaos Dergiades
Affiliation:
I. Zanna 27, Thessaloniki 54643, Greece e-mail: ndergiades@yahoo.gr
Quang Hung Tran
Affiliation:
High School for Gifted Students, Vietnam University of Science e-mail: tranquanghung@hus.edu.vn
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Extract

The Greek architect Kostas Vittas published in 2006 a beautiful theorem ([1]) on the cyclic quadrilateral as follows:

Theorem 1 (Kostas Vittas, 2006): If ABCD is a cyclic quadrilateral with P being the intersection of two diagonals AC and BD, then the four Euler lines of the triangles PAB, PBC, PCD and PDA are concurrent.

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Type
Articles
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The Mathematical Gazette , Volume 108 , Issue 571 , March 2024 , pp. 53 - 60
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Copyright
© The Authors, 2024 Published by Cambridge University Press on behalf of The Mathematical Association

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References

Vittas, K., Euler lines in cyclic quadrilateral, (2006), available at http://artofproblemsolving.com/community/c6h107997 Google Scholar
Ha, N. M., A proof of Vittas’ Theorem and its converse, Journal of Classical Geometry, 1 (2012) pp. 32–39,Google Scholar
Dergiades, N., Dao’s theorem on six circumcenters associated with a cyclic hexagon, Forum Geometricorum, 14 (2014) pp. 243–246.Google Scholar
Deaux, R., Introduction to the geometry of complex numbers, (illustrated edition), Dover (2008). Google Scholar