[alogo] 1. Similar shapes inscribable in a circle

Polygons (here triangles CDE and CAG) similar to each other w.r. to a common vertex (here C) and
inscribable in circles have the lines joining homologous vertices pass through the second intersection point of
their circumcircles (here point O).

[0_0] [0_1]

The key fact is that triangle (DCA) is similar to (CEG). The rotation-angle involved in the similarity about
the center C is equal to ang(ECG), by which also line CE is rotated so as to take a position along line CG.
Thus the angle GCA, by which triangle DCA rotates to obtain aposition such that its sides {CD,CA} go
along the sides {CE, CG} is equal to the angle of lines DA and EG, intersecting at a point O. Thus, GCOA
is a cyclic quadrangle.

[alogo] 2. Similar shapes inscribable in a circle (general case)

The figure below illustrates the general case of two similar cyclic polygons, the similarity being centered
at the common vertex A of the two polygons. All other homologous vertices of the two polygons define
lines passing through the other intersection point B of the two circumcircles.
The argument for the general case is the same with the previous one for the case of triangles.

[0_0] [0_1] [0_2] [0_3]
[1_0] [1_1] [1_2] [1_3]
[2_0] [2_1] [2_2] [2_3]

This key-fact on the circumcircles was at the basis of the discussion in the file SimilarlyGliding.html as
well as in the file Similarity.html , handling the foundamentals on Similarities.

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