[Some 'eccentric' corollary to the results on incircular conditions of a triangle appeared in the previous article:
Inellipses; isogonal conjugates; fish bases...]
For an arbitrary triangle, there exist three excircles: each of those contacts an edge of the triangle and two others at these extended parts. Moreover, it is possible to draw rays those start from the center of an excircle and to be composed into a flatly foldable structure at that point. The following example shows such angular relations at a (local) flatly foldable structure:
Thus, three flatly foldable structures at respective centers of excircles around a given triangle will be illustrated by:
[Let the above diagram print on a sheet of paper and cut its triangular region (colored in gray) away, then the paper with a (triangular) hole will be flatly folded with its creases of printed segments - as we have done it -]
A partial colored version of the above picture to show that half of three generalized fish bases are included in the diagram:
The three flatly foldable structures of generalized fish bases will be composed into the following respective diagrams and graphics:


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投稿者: kaishonashi
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