hello,

I know CAD can take a while because its computational cost, but sometimes wolfram mathematica just quits after an hour or less and leaves me with these dots where it should show the number completed. By the way, the "failed" result is from a previous run using different parameters

Here is the command typed out

N@CylindricalDecomposition[
  {
   b^2 - (c^2 - a^2) == 0,
   a >= 0,
   c > 0,
   t > 0,
   c > a,
   b > 0,
   pl - (pn + t*b/c + a + 2*a/b*t + t*c/b) == 0,
   d - (4 t + b + t*a/c) == 0,
   lb^2 + t^2 - ((pn + c)^2 + (d - 2 t)^2) == 0,
   lb - (2 a + 2*a/b*t + t*c/b) == 0,
   lb > 0,
   t - 13 == 0
   },
  {t, a, c, lb, pn, b, pl, d}
  ]