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Karakterizacija tetivnih štirikotnikov
ID Uršič, Nejc (Author), ID Vavpetič, Aleš (Mentor) More about this mentor... This link opens in a new window

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Abstract
Diplomska naloga obravnava karakterizacije tetivnih štirikotnikov. Tetivni štirikotnik je geometrijski lik, katerega oglišča ležijo na skupni krožnici. Naloga predstavi tako osnovne kot tudi manj znane karakterizacije. Vsem izrekom sledijo njihovi dokazi, v katerih so največkrat uporabljene lastnosti podobnih trikotnikov, skladnih kotov ter obodnih in središčnih kotov. Glavni poudarek naloge je na starem japonskem izreku, ki govori o karakterizaciji tetivnih mnogokotnikov. Dokaz slednjega izreka je s to nalogo prvič mogoče prebrati v celoti.

Language:Slovenian
Keywords:tetivni štirikotnik, konveksen štirikotnik, obodni kot, središčni kot, podobni trikotniki, očrtana krožnica, včrtan mnogokotnik
Work type:Bachelor thesis/paper
Typology:2.11 - Undergraduate Thesis
Organization:FRI - Faculty of Computer and Information Science
Year:2024
PID:20.500.12556/RUL-161563 This link opens in a new window
COBISS.SI-ID:213360643 This link opens in a new window
Publication date in RUL:12.09.2024
Views:176
Downloads:21
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Secondary language

Language:English
Title:Characterisation of cyclic quadrilaterals
Abstract:
This paper discusses characterizations of cyclic quadrilaterals. A cyclic quadrilateral is planar geometric object, whose vertices all lie on the same circle. The thesis describes and proves the basic theorems as well as some less known characterizations. All theorems are accompanied by proofs and proofs of converse. Those usually contain properties of similar triangles and congruent angles. For the proofs in this paper it is also necessary to understand the inscribed angle theorem. Paper takes a deeper look at the old Japanese theorem about cyclic polygons. For the first time it is possible to read the direct proof of the theorem and the proof of converse in the same place.

Keywords:cyclic quadrilateral, convex quadrilateral, inscribed angle, central angle, similar triangles, circumscribed circle, inscribed polygon

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