I'm looking for some opinions on a design question.

I've got an Ikea coffee table out of solid pine. In cross section, the
legs are a bit over 2" square. I'm planning on adding a shelf to the
table to make it easier to clean up when company comes over (or perhaps
more realistically, to accumulate more stuff).

The question that I've got is how to support the shelf, given that it
wasn't originally designed for one.

I was considering cutting a 3/4" high slot into the inside corner of
each of the legs. Viewed from above, the cutout would be about 1"
square, or about 1/4 of the total cross section of the leg.

What would you call this slot anyways? It's kind of like a mortise, but
it's on a corner, and there really isn't a matching tenon. Is it kind
of a wierd dado?

Has anyone seen anything like this? I expect I'd have to reinforce the
underside of the shelf, given that it will just be 3/4 pine.

Chris