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The three diagonal points of a complete quadrilateral are never collinear.
There are three theorems related to pedal circles that go under the collective title of the Fontené theorems. The first Fontené theorem lets DeltaABC be a triangle and P an ...
A 100-sided polygon, virtually indistinguishable in appearance from a circle except at very high magnification.
A 70-sided polygon.
A 60-sided polygon.
A 32-sided polygon. The regular icosidodecagon is a constructible polygon, and the regular icosidodecahedron of side length 1 has inradius r, circumradius R, and area A r = ...
A 24-sided polygon. The regular icositetragon is constructible. For side length 1, the inradius r, circumradius R, and area A are given by r = 1/2(2+sqrt(2)+sqrt(3)+sqrt(6)) ...
A 10000-sided polygon.
An 80-sided polygon.
The star polygon {8/3}.
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