publication . Article . 2016

Circumcenter, Circumcircle and Centroid of a Triangle

Roland Coghetto;
Open Access English
  • Published: 01 Mar 2016 Journal: Formalized Mathematics (issn: 1898-9934, Copyright policy)
  • Publisher: Sciendo
Abstract
<jats:title>Summary</jats:title> <jats:p> We introduce, using the Mizar system [1], some basic concepts of Euclidean geometry: the half length and the midpoint of a segment, the perpendicular bisector of a segment, the medians (the cevians that join the vertices of a triangle to the midpoints of the opposite sides) of a triangle. </jats:p> <jats:p>We prove the existence and uniqueness of the circumcenter of a triangle (the intersection of the three perpendicular bisectors of the sides of the triangle). The extended law of sines and the formula of the radius of the Morley’s trisector triangle are formalized [3]. </jats:p> <jats:p>Using the generalized Ceva’s Theo...
Subjects
free text keywords: 51M04, 03B35, Euclidean geometry, perpendicular bisector, circumcenter, circumcircle, centroid, extended law of sines, identifier: EUCLID12, version: 8.1.04 5.36.1267, Mathematics, QA1-939, Geometry, Cyclic quadrilateral, Circumscribed circle, Incircle and excircles of a triangle, Euler line, symbols.namesake, symbols, Isosceles triangle, Midpoint, Bisection
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publication . Article . 2016

Circumcenter, Circumcircle and Centroid of a Triangle

Roland Coghetto;