I stumbled onto the Three Circles and Common Tangents problem ( https://www.cut-the-knot.org/proofs/threecircles.shtml )on the Futility Closet blog. I just wanted to post the solution I came up with, because it made the collinearity immediately obvious to me:

See the three circles as three spheres of equal size, but projected in 3d, so the biggest circle represents the sphere that is closest to the viewer, and so on. Then, the three pairs of tangents define three infinitely long cylinders, which obviously (being in the same plane) have to recede towards the same horizon line l.