Two equal circles in the same plane cannot have the following number of common tangents.
$\textbf{(A) \ }1  \qquad \textbf{(B) \ }2 \qquad \textbf{(C) \ }3 \qquad \textbf{(D) \ }4 \qquad \textbf{(E) \ }\text{none of these}$
Two congruent coplanar circles will either be tangent to one another (resulting in $3$ common tangents), intersect one another (resulting in $2$ common tangents), or be separate from one another (resulting in $4$ common tangents).
Having only $\boxed{\textbf{(A)}\ 1}$ common tangent is impossible, unless the circles are non-congruent and internally tangent.