**(1) Dr. Veselin Nenkov, Assoc. Prof., (2) Stanislav Stefanov, PhD student, Haim Haimov, Researcher**

*(1) “Nikola Vaptsarov” Naval Academy
73, Vasil Drumev St.
Varna, Bulgaria*

*(2) Technical University – Sofia
1000 Sofia, Bulgaria*

**Abstract.** Formulae are derived and presented for the distances to the vertices
and the midpoints of the sides and diagonals of a quadrilateral from three of its
notable points. They are used to prove some inequalities in the quadrilateral,
connecting the lengths of its sides and diagonals. An interesting property of the
centroid of a quadrilateral inscribed in a circle has been found too.

*Keywords:* quadrilateral; notable points; inequalities; centroid; Euler circle

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