Bottema's theorem

Bottema's theorem is a theorem in plane geometry by the Dutch mathematician Oene Bottema (Groningen, 1901–1992).

, construct squares on any two adjacent sides, for example

The midpoint of the line segment that connects the vertices of the squares opposite the common vertex,

, of the two sides of the triangle is independent of the location of

[2] The theorem is true when the squares are constructed in one of the following ways: If

If the squares are replaced by regular polygons of the same type, then a generalized Bottema theorem is obtained: [3] In any given triangle

construct two regular polygons on two sides

on the circumcircles of the polygons, which are diametrically opposed of the common vertex

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