The theorem specializes for circles in the obvious way. For circles and triangles it reduces to Euler's condition on the radii of two circles: [ R^2 - 2*R*r = d^2 ] . R, r being the radii and d the distance of the centers of the two circles. The theorem asserts that this equation is necessary and sufficient in order that a triangle has the two circles as circumscribed and inscribed respectively. The specialization for circles and [Bicentric] (in EucliDraw called [Bicircular]) quadrangles is also known as [Theorem of Fuss]. The condition is: [ 1/r^2 = 1/(R+d)^2 + 1/(R-d)^2 ]. See the file Bicentric.html for a discussion of properties of these quadrilaterals.

For an apparently more complicated example of polygons with N sides see the file MaximalRegInEllipse.html .

DesarguesInvolution.html

Hart_Lemma.html

MaximalRegInEllipse.html

Poncelet_Proof.html

Tangent_Cuts_Circle.html

Tangent_Cuts_Envelope.html

Berger, M

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