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# Triangles, Spheres, and Circles

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Part of the Problem Books in Mathematics book series (PBM)

## Abstract

A triangle is a simplex (see 2.E) in a Euclidean affine plane, or, in other words, three non-collinear points x, y, z; we can write J = {x, y, z}. These three points are the vertices of J; we call sides the segments [y, z], [z, x], [x, y], and also their lengths, which are conventionally written a = yz, b = zx, c = xy. The angles of J are elements of ]0, π[, measured between oriented lines (cf. 8.F), and written $$A = \overline {\overrightarrow {xy} ,\overrightarrow {xz} } , B = \overline {\overrightarrow {yz} ,\overrightarrow {yx} } , C = \overline {\overrightarrow {zx} ,\overrightarrow {zy} } .$$. We also have the semi-perimeter p = (a + b + c) /2.

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## Copyright information

© Marcel Berger 1984

## Authors and Affiliations

1. 1.U.E.R. de Mathematique et InformatiqueUniversité Paris VIIParis, Cedex 05France
2. 2.Centre National de la Recherche ScientifiqueParisFrance
3. 3.P.U.K.GrenobleFrance