IMO Shortlist 1962 problem 6
Dodao/la:
arhiva2. travnja 2012. Consider an isosceles triangle. let
![R](/media/m/4/d/7/4d76ce566584cfe8ff88e5f3e8b8e823.png)
be the radius of its circumscribed circle and
![r](/media/m/3/d/f/3df7cc5bbfb7b3948b16db0d40571068.png)
be the radius of its inscribed circle. Prove that the distance
![d](/media/m/f/7/d/f7d3dcc684965febe6006946a72e0cd3.png)
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