+223 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.
