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undergraduate thesis
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The Euler Circle
Andrijana Blažević (2017)
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics
Algebra and Calculus Research Group
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Blažević, A. (2017). Eulerove kružnice (Undergraduate thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:361610

Blažević, Andrijana. "Eulerove kružnice." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. https://urn.nsk.hr/urn:nbn:hr:126:361610

Blažević, Andrijana. "Eulerove kružnice." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. https://urn.nsk.hr/urn:nbn:hr:126:361610

Blažević, A. (2017). 'Eulerove kružnice', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 20 February 2019, https://urn.nsk.hr/urn:nbn:hr:126:361610

Blažević A. Eulerove kružnice [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2017 [cited 2019 February 20] Available at: https://urn.nsk.hr/urn:nbn:hr:126:361610

A. Blažević, "Eulerove kružnice", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:126:361610

Metadata
TitleEulerove kružnice
AuthorAndrijana Blažević
Mentor(s)Zdenka Kolar-Begović (thesis advisor)
Abstract
U ovom radu proučavana je jedna kružnica pridružena trokutu. Kružnica na kojoj leže polovišta stranica trokuta, nožišta visina te polovišta dužina kojima je jedna krajnja točka vrh trokuta, a druga ortocentar trokuta poznata je kao Eulerova kružnica ili kružnica devet točaka. Važna svojstva ove kružnice su istražena. Dokazana je i tvrdnja koja povezuje Eulerovu kružnicu, trokutu upisanu kružnicu i trokutu pripisane kružnice, poznati Feuerbachov teorem.
KeywordsEuler circle inscribed circle escribed circle concyclic points
Parallel title (English)The Euler Circle
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Lower level organizational unitsChair of Pure Mathematics
Algebra and Calculus Research Group
PlaceOsijek
StateCroatia
Scientific field, discipline, subdisciplineNATURAL SCIENCES
Mathematics
Geometry and Topology
Study programme typeuniversity
Study levelundergraduate
Study programmeUniversity undergraduate study programme in mathematics
Academic title abbreviationuniv.bacc.math.
Genreundergraduate thesis
Language Croatian
Defense date2017-09-29
Parallel abstract (English)
In this paper, a circle that is joined to the triangle is studied. The circle which passes through the mid-points of the sides of a triangle, the feett of the altitudes and the mid-points of the line segments from the orthocenter to the vertices of a triangle is called Euler circle or the nine-point circle. Some important characteristics of this circle are researched. The assertion that links Euler circle to the inscribed and escribed circles of a triangle was proved. It is well known Feuerbach’s theorem.
Parallel keywords (Croatian)Eulerova kružnica upisana kružnica pripisana kružnica konciklične točke
Resource typetext
Access conditionOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
URN:NBNhttps://urn.nsk.hr/urn:nbn:hr:126:361610