[Jeff Higgins]

Clinchers have been around at least since I was a kid in the 1960's, used on every bike that is not a hard core road racing bike. "Sew-up" or "tubular" tires used to be the default on higher end road racing bikes but have long since been pretty much replaced by "clinchers" even for that use. I really doubt they even come as big as 35mm in cross section, the ones I had experience with were as narrow as 19mm, with the widest I remember being 23mm. I think it's a safe bet you have a clincher style rim. Just pull the tire off and look.