Yes, of course they need 90º angles, don’t know exactly what I was expecting, I think I’ll get more sleep today…

Unless…

I guess I felt there was something wrong about the “fact” that they couldn’t be joined with a circular arc -even though the premise was not to move or rotate them. So I have thought twice about it, and it can be done! They can’t be displaced but they have to be joined anyway, which means they will become a single larger plank… Thus, we can easily elongate the most distant of them from the targeted circle so that the perpendicular is equidistant with the other perpendicular. Note this is not breaking rules; it is actually what we are asked to do:

This is an example of the side of two planks that “can’t” be joined with a circular arc, in case it is useful for anyone initiating into this and/or not having enough sleep to figure it out:

We can’t rotate them or move the planks from their position (those parts are fixed to something else and the angle is also fixed) but we need to work with the space in between. As the circle would be tangent to just one of them…

…we need to enlarge the one whose distance to the circle center is shorter until it is equal. For symmetry purposes I have divided the angle formed by the two planks in two with the aid of a parallelogram (but as the planks have the same thickness their elongations already make one I could have better used). The point where this angle crosses the perpendicular from the plank that was further will be the new center of a circle that is tangent to both planks. I had to actually draw the line over the guide as the tangent or perpendicular indicator (the magenta color) didn’t show up with the guide (it did a couple of times but SU refused to do it again).

All this is surely trivial for those of you experts on this, but it may help people who are searching for the problem I posted which I’m actually managing to explain after reading @slbaumgartner and @Geo answers. Anyway, as it happens with most problems, if anyone is having a hard time with this, taking some quality rest would probably help you sorting things out and obviate this, but as all the previous answers have also saved me a lot of frustration, I thought maybe this could also help at least some having a hard time and in need of some rest…

Thanks again,