High Speed Signal on Large Circular Ring
Perhaps a graphic to really show what you mean would help, however, what I get from your description is something that will not work and cannot just be fixed by throwing some impedance matching or gold plating after the ring.

This is not just a matter of reflections or a weaker signal, but a 7-8 cm is a significant fraction of a wavelength (to even more than an entire wavelength, depending on the material properties you are dealing with). What you could get is a kind of bad and unpredictable rat-ring coupler, where part of the wave travels one way around the right, and part of it travels the other way. As they could be of different lengths, one will have a different phase shift than the other, and as a result you might actually get destructive interference. The only way I can imagine this working is if you cut your ring and make the connection points power divider/combiners, and terminating the ends at the cut.