As a limiting case of this construction, a line tangent to both circles, where the circles fall on opposite sides, passes through the internal homothetic center, as illustrated by the line joining the points B 1 and A 2 in Figure 3.
As a limiting case of this construction, a line tangent to both circles passes through one of the homothetic centers; see tangent lines to two circles for details. If the circles fall on opposite sides of the line, it passes through the internal homothetic center, as illustrated by the line joining the points B 1 and A 2 in Figure 3.