De or het ruilkring?

The correct Dutch article is:

de ruilkring

Rule Words ending in -ing: almost always de. See the rule

How to use ruilkring

the ruilkringde ruilkring
this ruilkringdeze ruilkring
that ruilkringdie ruilkring
our ruilkringonze ruilkring
your ruilkringjouw ruilkring
every ruilkringelke ruilkring
which ruilkring?welke ruilkring?
a big ruilkring / the big ruilkringeen grote ruilkring, de grote ruilkring