Four Theorems on Spherical Triangles

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Draw a spherical triangle on the surface of a unit sphere centered at
. Let the sides opposite the corresponding vertices be the arcs
,
,
. Let
,
,
be the angles at the vertices
,
,
;
,
,
are also the dihedral angles of a trihedron
with apex
and edges
,
,
. Let
,
,
be the angles of
at
. Let
,
,
be points on the sides (or their extensions) opposite to
,
,
. Define the unit vectors
,
,
.
Contributed by: Izidor Hafner (March 2017)
Open content licensed under CC BY-NC-SA
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This Demonstration is based on problem 5.34 in [3, p. 88].
References
[1] Wikipedia. "Spherical Law of Cosines." (Mar 15, 17) en.wikipedia.org/wiki/Spherical_law_of _cosines.
[2] Wikipedia. "Spherical Trigonometry." (Mar 15, 2017) en.wikipedia.org/wiki/Spherical_trigonometry.
[3] V. V. Prasolov and I. F. Sharygin, Problems in Stereometry (in Russian), Moscow: Nauka, 1989.
[4] Wikipedia. "Ceva's Theorem." (Mar 15, 2017) en.wikipedia.org/wiki/Ceva%27 s_theorem.
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