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• Charakteristische Dreieckpunkte in der projektiv-erweiterten hyperbolischen Ebene

  299-315

  Ana Sliepčević

  Ivanka Babić

  Views:

  9

  Some basic planimetric constructions regarding segments, angles and triangles are shown in the Cayley-Klein model of the hyperbolic plane. Relationship with the situation in the Euclidean plane is given. H-triangles are classified considering the location of their vertices and sides with respect to the absolute. There are 28 types of triangles. It is shown that there exist 12 pairs of dual triangles, while 4 types of triangles are dual to themselves. For every type of triangle the existence and number of the characteristic points are determined. Few examples of triangles with construction of their characteristic points, incircles and circumcircles are given.

• Über ähnliche Aufsatzdreiecke einer Strecke

  337-348

  Oswald Giering

  Views:

  28

  In this article we investigate (with methods of school geometry) a figure (PQ,ABC) consisting of three given similar triangles PQA, PQB, PQC with side PQ in common (Figure 1). We combine other triangles with this figure such as triangle ABC which is proved to be similar to the given triangles. The incircles of three additional triangles adjacent to triangle ABC will be determined.