If you cut the corner of the beged on an angle, you end up with a beged of 5 corners and you need tzitzit in four of the corners. But if you round off a corner then you only have 3 corners and the beged is pattur from tzitzit.

The Aruch Hashulchan in OC 10:13 says that it's not enough to cut a very small piece of the corner, but rather you need to cut enough that the edge between the two new corners is a tefach, or at least 3 etzaba'ot. Fine. But then he says if you're rounding the corner it needs to be discernable enough that "hemshech ha-iggul saviv yihiyeh 3 tefachim". What does he mean by that? That the segment of the circle that is the rounded corner of the beged must be such that were you to continue the circle the circumference would be 3 tefachim? But still, if the center of that circle is further from the corner then it's different than if the center of that imaginary circly is closer to the corner.

I think it means that the rounded area should be 3 tfachim long.

3 tefachim is a really big arc. I doubt when most people round off a corner [eg. on a blanket] they do so such that it's 3 tefachim along the rounded edge. And anyway, that's at least three times the length of the edge he would require if you're cutting a corner to make 5 corners. It just seems to me to be out of proportion.

I don't know how big it is, but when my father wears a rain coat, it's VERY obvious that he's got an arc in one corner.