Commit with one character YAML difference? Check.
Commit with 2-3 YAML lines just to add the right logging? Check.
Wait 5+ minutes for a YAML diff to propagate through our test pipeline for the nth time today? .. sigh .. check
BUT, after ironing all these things out (and running our own beefy self-hosted runner which is triggered to wake up when there's a test process to snack on), it's .. uh.. not so bad? For now?
Much more elegant: consider every circle that fits inside the unit circle, and we will work backward to find combinations of points. We only need consider centers on the x axis by symmetry, so these are parameterized by circle center at (0,c) and radius r with 0<c<1 and 0<r<1-c. Each circle contributes (2 pi r)^3 volume of triples of points, and this double integral easily works out to 2 pi^3/5 which is the answer (after dividing by the volume of point triples in the unit circle, pi^3)