More Circles

I'm working on the "inner square" thing. I know you already know it. I should be able to deduce this pretty quickly. But one of the answers I'm getting I don't trust, so I'm continuing to work it.

In the meantime, here's something I recall from my youth. This came from a Scientific American. It turns out if you draw three circles of not equal radius, and position them on a plane such that the three centerpoints of the circles do not themselves form a line, then the lines that run tangent to the circles will converge to three points which, together, fall in a line:



Drawing the Powerpoint was easy. Proving this is another matter. As a kid I struggled and struggled and never did prove it. The answer came the next month's issue. I can't recall the specifics, but it had something to do with taking this concept to three dimensions. The tangent lines are then cones, and the convergence points of the cones fall onto a plane.

I would have figured it out but I was too interested in the brunette chick on the school bus.