600D - Area of Two Circles' Intersection requires careful treatment of loss of significance, more than the geometry itself.

Let's review the geometry, first. We need three numbers (r₁, r₂, d); where d is the distance between two centers,

The intersection is determined from two circular sectors subtracted by two triangles, yielding

where angles θ₁ and θ₂ are determined from the cosine formula

So far, so good. Perhaps you just throw in numbers and compute in long double precision. I guess the tests were created this way. But... wait!