with a curved piece of same thickness, so that they look similar to this other one I created before:

For this one I created the curved side first and then I just extruded (pulled) it. I may delete the 3D faces and work the same way; the issue is that for the one I managed to make the bent, the curve length was arbitrary but I now need them to keep the distance and shape/thickness fixed as much as possible, i.e. the corners that are going to be joined with arcs should be the same thickness and distance than the rest of the plank, or at least as much as possible. I can’t figure out how to do that; is it actually possible? In case it is not, is there any way to approximate that?

I think the answer depends on how you placed the two planks. If they are “nicely” located and oriented, you can create construction lines through the thin edges of the two planks next to the gap and these lines will intersect at the center of circular arcs that will do what you want. If they are not nicely located you won’t be able to use circular arcs and will have to do something quite a bit more complicated.

Guau! Steve, Geo, Box, Cotty, your answers are so useful to me! Wish I had found this sooner.

I understand “nice” (as @slbaumgartner says) means mostly symmetrical… of course I couldn’t make a tangent circle if they were not symmetrical, which is the same to say, that both corners from were the tangent is going to cross have the same radio/distance to center of the arc/circle. I thought I was doing exactly as you say and depict @Geo, just tracing 90º lines from the corners to find the center of the arc to be drawn with the simple Arc tool, but I have realized I was wrongly assuming the lines/rectangles would be at the same distance because they just looked like such.

So as the two rectangles are already given and I can’t rotate or move some of them (but in some cases I can) I have two options: search for my technical drawing class at school how to find the center for the tangent circle (surprisingly I wasn’t able to find info about how to do this on the internet but maybe I wasn’t clear about what to search when I tried it)
or installing the plugins @Box and @Cotty have pointed out, which seems much easier (finished school many many years ago). Even though I still need an arc (a symmetric or circular curve) in some cases (anyone knows of a link explaining it?), I could use bezier curves with those so really useful for-me plugins in many of them.

Don’t break your head too much looking for your old class notes! Tangents always form a 90 degree angle with the radius where they touch the circle, so if what I described and @Geo illustrated doesn’t do it, there is no way to construct a circle tangent at the ends of both planks. You will either have to move/alter a plank or use something other than a circular arc.

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…

Another approach. ARC tool does not create true tangents, the Bezier order three does, The model was created first just two intersecting lines, rotted one up 25 degs,create the curve between , use offset tool to make 4" thick, then pp tool tool to make width you want bent board.skp (43.7 KB)

One of the best parts of SU is the inference engine, you can pretty much work without bothering with drawing guides and such.
I haven’t specified the radius of the arc here but the radius point is easily drawn using the magenta inference.

The broken link issue is happening to everyone and has been reported to the forum administrators. What @mac7595 means is that classic Bezier curves are based on cubic polynomials, whereas circles are quadratic. Alas, the notion of “true tangents” is problematic in SketchUp since there are no true curves, only sequences of straight edges. This applies equally to Bezier curves as to circular arcs. The best one can do is “would have been a true tangent if SketchUp drew the abstract curve defined by the math instead of a representation using a sequence of edges”.