#[Taxi][1], 1582 bytes

    Go to Post Office:w 1 l 1 r 1 l.Pickup a passenger going to The Babelfishery.Pickup a passenger going to Tom's Trims.Pickup a passenger going to Tom's Trims.Go to Tom's Trims:n.[a]Go to Post Office:s.Pickup a passenger going to The Babelfishery.Go to The Babelfishery:s 1 l 1 r.Pickup a passenger going to What's The Difference.Pickup a passenger going to What's The Difference.Go to What's The Difference:n 5 l.Pickup a passenger going to Cyclone.Go to Cyclone:e 1 r.Pickup a passenger going to Multiplication Station.Pickup a passenger going to Multiplication Station.Go to Multiplication Station:s 1 l 2 r 4 l.Pickup a passenger going to Addition Alley.Go to Tom's Trims:s 1 r 3 r.Pickup a passenger going to The Babelfishery.Switch to plan "b" if no one is waiting.Switch to plan "a".[b]Go to Addition Alley:n 1 r 1 l 3 l 1 l.Pickup a passenger going to Magic Eight.Go to Post Office:n 1 r 1 r 3 r 1 l.Pickup a passenger going to The Babelfishery.Go to The Babelfishery:s 1 l 1 r.Pickup a passenger going to Addition Alley.Pickup a passenger going to Addition Alley.Go to Addition Alley:n 5 l 1 l.Pickup a passenger going to Cyclone.Go to Cyclone:n 1 l 1 l.Pickup a passenger going to Multiplication Station.Pickup a passenger going to Multiplication Station.Go to Multiplication Station:s 1 l 2 r 4 l.Pickup a passenger going to Magic Eight.Go to Magic Eight:s 1 r.Switch to plan "c" if no one is waiting.'1' is waiting at Writer's Depot.[c]'0' is waiting at Writer's Depot.Go to Writer's Depot:w 1 l 2 l.Pickup a passenger going to Post Office.Go to Post Office:n 1 r 2 r 1 l.

[Try it online!][2]

Outputs `1` for overlapping circles.   
Outputs `0` for non-overlapping circles (including tangential circles).   


Ungolfed / formatted:

    Go to Post Office: west 1st left 1st right 1st left.
    Pickup a passenger going to The Babelfishery.
    Pickup a passenger going to Tom's Trims.
    Pickup a passenger going to Tom's Trims.
    Go to Tom's Trims: north.
    [a]
    Go to Post Office: south.
    Pickup a passenger going to The Babelfishery.
    Go to The Babelfishery: south 1st left 1st right.
    Pickup a passenger going to What's The Difference.
    Pickup a passenger going to What's The Difference.
    Go to What's The Difference: north 5th left.
    Pickup a passenger going to Cyclone.
    Go to Cyclone: east 1st right.
    Pickup a passenger going to Multiplication Station.
    Pickup a passenger going to Multiplication Station.
    Go to Multiplication Station: south 1st left 2nd right 4th left.
    Pickup a passenger going to Addition Alley.
    Go to Tom's Trims: south 1st right 3rd right.
    Pickup a passenger going to The Babelfishery.
    Switch to plan "b" if no one is waiting.
    Switch to plan "a".
    [b]
    Go to Addition Alley: north 1st right 1st left 3rd left 1st left.
    Pickup a passenger going to Magic Eight.
    Go to Post Office: north 1st right 1st right 3rd right 1st left.
    Pickup a passenger going to The Babelfishery.
    Go to The Babelfishery: south 1st left 1st right.
    Pickup a passenger going to Addition Alley.
    Pickup a passenger going to Addition Alley.
    Go to Addition Alley: north 5th left 1st left.
    Pickup a passenger going to Cyclone.
    Go to Cyclone: north 1st left 1st left.
    Pickup a passenger going to Multiplication Station.
    Pickup a passenger going to Multiplication Station.
    Go to Multiplication Station: south 1st left 2nd right 4th left.
    Pickup a passenger going to Magic Eight.
    Go to Magic Eight: south 1st right.
    Switch to plan "c" if no one is waiting.
    '1' is waiting at Writer's Depot.
    [c]
    '0' is waiting at Writer's Depot.
    Go to Writer's Depot: west 1st left 2nd left.
    Pickup a passenger going to Post Office.
    Go to Post Office: north 1st right 2nd right 1st left.



  [1]: https://bigzaphod.github.io/Taxi/
  [2]: https://tio.run/##1VSxbsIwEN3zFScWJiwSoNBstFSdUJFAYkAMxjjJqcaOYiPK11OHGAkIEKBTB8vy@e787t07G/qDu92nAqNgpLSBryhCxsMN@CDsyvKdjJB9r1OgkFKtuYx5BrFCGedRk4TDG11wEaFOeLa97axWdQ2TDFf6br8C3JEllGRG52XM@jGcLu@ZOdSHym9mmybU5Hhs9ACjiGdcMv5ERAHi4l0ooVPB/fuWCSUPWdwp5JXoh2thMBXIqEElYWz2@zMhxcuXLx2VgRVRu6KQ/nKJ@9C@EHx7oeV6r8VWRV2lHo83aFiSX6WCSqgtaoARSAWWJ0ANG2qflXHJj9bIbOEkdorNdsVNhUUjKqdjSGNk8IFxYkhZsYdc@8oen7Q/KfiM8oe7U6KlcwcdlwUrHWDxv0Rb7u2RpVBsSVjsigDrfv3oCNTANEPDMzsAA54qQ2ZsXm9W@LjP5MTofvKgopYjVV7VaeA0utu9klbgNbqk2/UC0vNeSOB7jR7p@F6TtH8B