Generalizations of Hagge's Theorems

Details Generalizations of Hagge's Theorems Generalizations of Hagge's Theorems

2010-07-16

arxiv.org/abs/1007.2762v1

Mathematics

Metric Geometry

12 pages, 5 figures

Scientific paper

Two generalizations of Hagge's theorems are described. In the first we consider what happens when one moves from the orthocentre to a general point. What one loses by doing so is the indirect similarity and hence one loses the centre of indirect similarity. Instead one proceeds from the centre of the circle under consideration. In the second generalization we consider pairs of triangles that have orthologic centres with respect to each other, so that an indirect similarity is the main feature preserved.

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