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The ratio of the radii of the circles of a triangle

The applet allows to investigate the relation between the ratio of the radius of the circle circumscribing a triangle (R), and the radius of the circle inscribed in it (r). In the applet 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. In addition, the screen shows the angles and , which allow one to specify for which triangle one obtains the minimal value of the radius ratio.