Two circles with radius $1$ are externally tangent at $B$, and have $\overline{AB}$ and $\overline{BC}$ as diameters. A tangent to the circle with diameter $\overline{BC}$ passes through $A$, and a tangent to the circle with diameter $\overline{AB}$ passes through $C,$ so that the tangent lines are parallel. Find the distance between the two tangent lines.