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Extra distance on a curve

We've probably all had measurements where there are cars or other objects on a course that cause you to ride farther out from the curb than 20cm. On a straight section, no big deal, just do an offset until past the obstacle.

But on a curved section, riding wide has the effect of making the measurement longer and thus shortening the actual course.

I'm sure there's a mathematical trick to figuring out what this extra distance is, no doubt involving Pi (Pete Riegel was great at this). Anyone have a quick and dirty formula for this?

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