Finding External Tangent Points for Two Circles

[Update: 10-21-2012: The geometry discussed in this post has been superseded by the discussion about path planning for Dubin’s Cars:] I recently had a geometry problem I needed to solve involving finding tangent lines to two circles. If you’re like me, you don’t remember all the geometry you learned in school. And if you’re like me, you prefer searching the internet for answers versus turning to your books. I looked and looked online, but couldn’t really find a satisfying guide on finding the tangent points for two circles. Right now, even the Wikipedia page is a mess. How exactly does one “equate theta” and then “add x-y coordinates of a triangle” to a point? Perhaps in the future this will improve, but for now, here’s how I figured it out. I’m only going to run through finding one external tangent point. Figuring out the others as well as the tangent lines should become trivial afterwards.

Continue reading “Finding External Tangent Points for Two Circles”