Yes, in this case a numeric approach would probably be the way to go:
- Assume that R1, R2 are the radii of the discs and A_ORIG is the original area (eg. R1^2 PI)
- Calculate the area A for a given R1, R2
- Multiply R1 and R2 with SQRT(A_ORIG / A)
- Repeat
If this doesn't converge after a few iterations, you can use the Newton method, or even a simple binary search to find he correct radii very quickly. A(k R1, k R2) should be monotonic for k, so solving it numerically for a given value should be trivial.
- Assume that R1, R2 are the radii of the discs and A_ORIG is the original area (eg. R1^2 PI)
- Calculate the area A for a given R1, R2
- Multiply R1 and R2 with SQRT(A_ORIG / A)
- Repeat
If this doesn't converge after a few iterations, you can use the Newton method, or even a simple binary search to find he correct radii very quickly. A(k R1, k R2) should be monotonic for k, so solving it numerically for a given value should be trivial.