



 
Maty, You need more information. In general you need three pieces of information to fix a triangle. Even if you are given the radii of both the inner and the outer circles, there would be infinitely many different sized triangles inscribed in the larger circle and circumscribed about the smaller. We have attached an interactive picture. You can adjust the radius of either circle and drag the vertex A about the larger circle. Note that as A moves, the area of triangle ABC changes even though the incircle and circumcircle stay fixed. The largest and smallest are the isosceles triangles with one vertex on the line OI.
Created with Cinderella Chris  


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