IMO Shortlist 1962 problem 6
Dodao/la:
arhiva2. travnja 2012. Consider an isosceles triangle. let
be the radius of its circumscribed circle and
be the radius of its inscribed circle. Prove that the distance
between the centers of these two circle is
%V0
Consider an isosceles triangle. let $R$ be the radius of its circumscribed circle and $r$ be the radius of its inscribed circle. Prove that the distance $d$ between the centers of these two circle is $$d=\sqrt{R(R-2r)}$$
Izvor: Međunarodna matematička olimpijada, shortlist 1962