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A triangle with rational sides and rational area is called a rationaltriangle. In this paper we consider three problems of finding pairs of rationaltriangles which have a common circumradius as well as either a common perimeteror a common inradius or a common area. While several similar problemsconcerning pairs of rational triangles have been considered in the existingliterature, these three problems have not been studied till now. For each ofthese problems, we give a parametric solution and we also indicate howadditional parametric solutions of these problems may be obtained.

Some diophantine problems concerning a pair of rational triangles with a common circumradius