Geodesic
The variety of generalizations of the Ptolemy's theorem
Dalʹnevostočnyj matematičeskij žurnal, Tome 19 (2019) no. 2, pp. 129-137

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The article examines the metric properties of a tetron. In particular case a tetron is a triangle, flat or spatial quadrangle, and also a tetrahedron. The main theorem is proved about the connection of the lengths of the sides, the magnitudes of the plane angles and the magnitude of the dihedral angle of the tetron is proved. Many remarkable theorems about triangles, quadrangles, and tetrahedra are the corollaries of this theorem. Special attention given to equihedral tetrahedra. 
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     author = {N. S. Astapov and I. S. Astapov},
     title = {The variety of generalizations of the {Ptolemy's} theorem},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {129--137},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2019_19_2_a0/}
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N. S. Astapov; I. S. Astapov. The variety of generalizations of the Ptolemy's theorem. Dalʹnevostočnyj matematičeskij žurnal, Tome 19 (2019) no. 2, pp. 129-137. http://geodesic.mathdoc.fr/item/DVMG_2019_19_2_a0/