In this sort of problems rounding errors could be the source of problems. That's why you shall avoid using float types here. The problem is completely solvable in integers.

There is something else. My code checks turning before B but still got WA on #5.

Sounds too complex.
If we replace C, D with their orthogonal projection on AB, then all steps except first collapse to only one step (check D = C*a, a > 1).

Still too complex, though. Over 20 lines in Python. There should be more simple solution...

Edited by author 26.12.2017 04:30

No lengths or projections XY, etc. Using scalar product (sp) and triple product (tp) it is at most five conditions:

  sp(ab,cd) == 0 and tp(ab,bc,cd) == 0 and # ⟂ and planar
  sp(ab,bc) >= 0 and # C after B
  sp(cd,bc) >= 0 and # BC goes in direction of CD
  sp(cd,bd) >= sp(cd,bc) # D after C

Something like AB and CD are orthogonal and complanar and there is no right such point E,  that E lies on AB-line,  E lies on CD line and the angle AED is ninety degrees.