[ Concentric Circles ] [ Tangent Circles ]

Find the radius of the circle that is tangent to two concentric circles with radii 3 and 5.

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There are two possible cases: a) the desired circle touches the smaller of the given circles externally and the larger one internally (Fig.1); b) the desired circle touches both given circles internally (Fig.2). In the first case, the radius of the desired circle is $\frac{5-3}{2}=1$. In the second case, it is $-\frac{5+3}{2}=4$.

## Problem