If we know the inradius $r$ of a triangle and the circumradius $R$ we can find out the distance between the incircle $I$ and the circumcircle $O$: $OI^2 = R^2-2Rr$. Therefore we can draw the incircle and the circumcircle, and their relative position is fixed. Making some drawings suggests that we can construct $ABC$ in a unique way starting from $R,r$.
Is there only one triangle $ABC$ (up to isometry) which has inradius $r$ and circumradius $R$? If yes, how do we draw it?
On
The question you asked is the special case of so- called Poncelet's porism. It says, that if you have two conics on the plane and one can find a $n-$gon for which one conic is inscribed and the other one is circumscribed in it, then one can find infinitely many such $n-$ gons. See this wikipedia article for the details Poncelet's porism
This can't be true, since there is a three-dimensional space of triangles up to isometry (parametrized by their side-lengths, which only need to satisfy the triangle inequality), and you only give me two parameters. A better question is then: what is the family of triangles with the same in- and out- radii.