Formulaes for the Distances from the Brocardians and the Miquel Point in a Quadrilateral to Its Vertices and the Midpoints of Its Sides and Diagonals

(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

Свързани статии:

Participation of the Battalions of the 11th Marching Regiment in the Battles for the Control of the Fortified Positions in the Area of the Town of Machin in January 1917 Hıstory Educatıon between the Major Reforms in Bulgarıan Educatıon 1948 – 2002 The 17th Century and the Barriers of Time: Nahiya Kara Lom in the Face of Economic and Demographic Crisis Sirma Danova (12.11.1984 – 22.10.2023)