Triangles with given inscribed and circumscribed circles. (Trianglar med givna omskrivna och inskrivna cirklar.) (Swedish. English summary)

Normat. 57, No. 3, 129-140 (2009).

Summary: This is a second article [for a review of the first one see ibid. 57, No. 1, 10‒21 (2009; Zbl 1188.51007; ME 2009f.00485)] in a series of three, concerning 1-dimensional families of triangles. In this case those with given circumscribed and inscribed radii $R,r$ are presented. The construction of such families is a special case of Poncelet’s theorem, exploiting the approach via elliptic curves, initiated by Jacobi.