Lev Emelyanov and Tatiana Emelyanova, Euler's Forumla and Poncelet's Porism,

Forum Geometricorum, 1 (2001) 137 -- 140.

Abstract:   It is well known that two intersecting circles O(R) and O_1(R_1) are the circumcircle and an excircle respectively of a triangle if and only if the Euler formula  d^2=R^2+2RR_1, where d=|OO_1|, holds. We present a possibly new proof and an application to the Poncelet porism.

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