Perhaps a good starting point would be to look at a "chord"[1], which is a line segment between two points on a circle. Then you'd look at a chord that is tange

Perhaps a good starting point would be to look at a "chord"[1], which is a line segment between two points on a circle. Then you'd look at a chord that is tangent to the inner circle of a set of two concentric circles. You can find the length of the chord from the radii of the circles. But what you're asking about is more general. You are looking for some sort of shortest path between two parallel curves [2]. Which seems like it would be a tricky problem to solve. Are you considering physics here? If you are, you are basically looking at a "racing line" [3]. And that's a complicated problem since it involves a lot of physics and engineering. You can't look at a single turn in a track and determine the best racing line. That's because the best racing line for a specific turn depends on the best racing lines of the nearby turns. You'd have to look at the track as a whole. There are entire theses written on this topic [4]. But a highway road is not the same as a racing track. In highway engineering they often use the Euler Spiral [5] to construct the turns, because of its nice properties. Funny enough, Euler Spirals play a role in optimizing your entry into turns on a track [6]! I think those might be some good jump-off points for further inquiry. [1]: https://en.wikipedia.org/wiki/Chord_(geometry) https://en.wikipedia.org/wiki/Chord_(geometry) [2]: https://en.wikipedia.org/wiki/Parallel_curve https://en.wikipedia.org/wiki/Parallel_curve [3]: https://en.wikipedia.org/wiki/Racing_line https://en.wikipedia.org/wiki/Racing_line [4]: https://dspace.mit.edu/bitstream/handle/1721.1/64669/706825301-MIT.pdf https://dspace.mit.edu/bitstream/handle/1721.1/64669/7068253... [5]: https://en.wikipedia.org/wiki/Euler_spiral https://en.wikipedia.org/wiki/Euler_spiral [6]: https://en.wikipedia.org/wiki/Euler_spiral#Auto_racing https://en.wikipedia.org/wiki/Euler_spiral#Auto_racing