Displaying similar documents to “Degree of triangle centers and a generalization of the Euler line.”

Rotation indices related to Poncelet’s closure theorem

Waldemar Cieślak, Horst Martini, Witold Mozgawa (2015)

Annales UMCS, Mathematica

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Let CRCr denote an annulus formed by two non-concentric circles CR, Cr in the Euclidean plane. We prove that if Poncelet’s closure theorem holds for k-gons circuminscribed to CRCr, then there exist circles inside this annulus which satisfy Poncelet’s closure theorem together with Cr, with ngons for any n > k.

Circumcenter, Circumcircle and Centroid of a Triangle

Roland Coghetto (2016)

Formalized Mathematics

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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. 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...

Morley’s Trisector Theorem

Roland Coghetto (2015)

Formalized Mathematics

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Morley’s trisector theorem states that “The points of intersection of the adjacent trisectors of the angles of any triangle are the vertices of an equilateral triangle” [10]. There are many proofs of Morley’s trisector theorem [12, 16, 9, 13, 8, 20, 3, 18]. We follow the proof given by A. Letac in [15].