I was trying to make an arc that is tangent to two planar lines with a specific radius. This is what I did:

From the point of intersection (O) of the two lines, go out the same arbitrary distance on each line, and from these points (A and A’), draw a perpendicular line to each of the lines.

From the intersection point (O’) of these two new lines, draw a line to the intersection point (O) of the original lines. (this line (O-O’) bisects the angle between both sets of lines)

On one of the new lines (A-O’ or A’-O’), from the new intersection point (O’), locate the point (B or B’) that is the distance of the known radius ®.

From this point (B or B’), draw a line that is parallel to the bisecting line (O-O’), to the associated original line (O-A or O-A’). The intersection point will be (C or C’)

Strike an arc of the known radius ®, centered on (C or C’) that crosses the bisecting line (O-O’) at two points (D and D’)

Using the point (D) as the center, the desired arc may now be drawn. (Centering on D’ will not create a tangent arc)

What I find is that the arc does not always connect to both lines (I see this by zooming in). When I create D and D’ from both sides, I see that the arcs do not intersect on the intersecting line (O-O’)

Granted, these errors are minuscule, but they will prevent faces from being automatically created.

And, granted, because I’m using the free version, I will live with it. Does the paid version have this problem, too?

Sketchup, Pro, Make and Web all use segments to create circles, this makes correct tangents difficult. There is at least one extension for creating correct tangents, but as you are using the web version, it is unavailable to you.

In the web version without having extentions available you can still adjust the radius (up to a certain amount of time or side tracking other SketchUp actions) in ‘Entity Info’. The ‘Tangent to’ arc adjusts to the new radius.
There must be no edge intersecting geometry between the ‘Tangent points’ and the point (real or virtual) O (intersection of both original edges) in your example.

@g.h.huber Thank you for the great tip! Being self taught, I certainly missed that one! I my case, though, my radius is fixed. I’m designing a curved block wall which has a minimum radius of 5 feet. Yes, I’m ■■■■ retentive. I’ll try to chill.

Then use that radius as input. Share an example where you can’t use what was suggested.
Unless you need more precision than __.six figures. (as in say R=34.0000007)

They vary, all obtuse. I want to keep the angle to a minimum. These are terrace walls and where the curves I will have to dig out more or fill in more as they go in and around the hill side.

I only used the default 12-segment arc but you could increase the number of segments. For the application, though, I expect 12 segments will be plenty unless you are measuring soil removal or fill in ounces.

@g.h.hubers When I first saw your tip, I thought I’d just file it away and use it another day. But your insistence inspired me to try it out. I couldn’t follow what you suggested, though. I missed something, there was no “make tangent to” in entity info. I think I’m being obtuse (couldn’t resist the pun).

But along the way I saw, in entity info, that I could change the number of segments! So when I did it my way, as I made an arc, I changed the segments of the arc to a very high number. This appeared to nail it. (another bad pun, sorry.)

And I learned an easy way (and I see DaveR has one, too!)

What I was saying is the arc stays tangent even when changing the radius in ‘Entity Info’. The arc slides along both edges, keeping it’s tangent property, when doing so. Opposed to when when changing the radius later. Then the ‘at first tangent points’ remain fixed intersections. Changing the radius may still be possible but the arc just expands or shrinks in place.

Changing the number of segments is always possible if ‘Entity Info’ says it’s an arc.

Well, that is how I created the arc.
Apparently SketchUp now keeps its focus on the arc’s property longer than in previous versions.
My warning was more like: if you need a different tangent radius, do so now. Later you may find that the connection vertices on both sides may be fixed locations. For how long you can still change the tangent arc is to be found out by someone with lots of patience

I suppose you need to correct/restore the “auto break edges” for the visual arc<>edge intersection(s) first.
If SketchUp automatically does that for you, it will break the "keep tangent while changing radius" option much sooner.