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Extensions of Vittas’ Theorem

Published online by Cambridge University Press:  15 February 2024

Nikolaos Dergiades
I. Zanna 27, Thessaloniki 54643, Greece e-mail:
Quang Hung Tran
High School for Gifted Students, Vietnam University of Science e-mail:


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.

© The Authors, 2024 Published by Cambridge University Press on behalf of The Mathematical Association

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Vittas, K., Euler lines in cyclic quadrilateral, (2006), available at Google Scholar
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Dergiades, N., Dao’s theorem on six circumcenters associated with a cyclic hexagon, Forum Geometricorum, 14 (2014) pp. 243246.Google Scholar
Deaux, R., Introduction to the geometry of complex numbers, (illustrated edition), Dover (2008). Google Scholar