Cevians as sides of triangles.
Čerin, Zvonko (2000)
Mathematica Pannonica
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Čerin, Zvonko (2000)
Mathematica Pannonica
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Paulus Gerdes (2003)
Visual Mathematics
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Miguel de Guzmán (2001)
RACSAM
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A simple proof is presented of a famous, and difficult, theorem by Jakob Steiner. By means of a straightforward transformation of the triangle, the proof of the theorem is reduced to the case of the equilateral triangle. Several relations of the Steiner deltoid with the Feuerbach circle and the Morley triangle appear then as obvious.
Čerin, Z. (1997)
Mathematica Pannonica
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Stammler, Ludwig (1997)
Beiträge zur Algebra und Geometrie
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Bukor, József (2008)
Annales Mathematicae et Informaticae
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Tomohide Hashiba, Yuta Nakagawa, Toshiyuki Yamauchi, Hiroshi Matsui, Satoshi Hashiba, Daisuke Minematsu, Munetoshi Sakaguchi, Ryohei Miyadera (2007)
Visual Mathematics
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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.
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...
Čerin, Zvonko (2000)
Mathematica Pannonica
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Maligranda, Lech (2008)
Banach Journal of Mathematical Analysis [electronic only]
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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].
Kolar-Begović, Z., Kolar-Šuper, R., Beban-Brkić, J., Volenec, V. (2006)
Mathematica Pannonica
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