Two tangent circles

Examine how the circles $x^2 + y^2 = 1$ and $(x - 3)^2 + y^2 = 4$ are placed. Their centers are $(0, 0)$ and $(3, 0)$ with radii $1$ and $2$. The distance between the centers is $3$, equal to the sum of the radii $1 + 2 = 3$.

When the distance between centers equals the sum of the radii, the two circles share exactly one point on the outside (external tangency). The tangent point lies on the segment joining the centers, a distance $1$ from $(0, 0)$ toward $(3, 0)$, namely $(1, 0)$. The large dot marks this point of tangency.