The ratio between R and r
The applet allows to find the minimal value of the ratio of the radius of the circle circumscribing a triangle (R), and the radius of the circle inscribed in it (r). One can drag the vertices of the triangle, and thus change the lengths of its sides. In each stage the screen shows the circumscribing and inscribed circles, their centers and the ratio between their radiuses. Thus one can discover that the minimal value of t=R/r is 2 and it is obtained for an equilateral triangle.