@DaveBryce, you beat me to the punch. If all you need is a profile with a double tangent round or fillet, you COULD build two intersecting planes, round or fillet them using that extension, then cut across the result for the 2D representation. Lots of work, but hey, there are lots of operations in SketchUp that need workarounds. The only problem I’ve found with using Round Corner, is that the point where the curve begins isn’t always on a perpendicular to the tangent edge from the center of arc. A situation that shows up using Follow Me to perform rounds or fillets, and which is not unique to SketchUp. The extrusion tool in AutoCAD did that too. My guess is that it’s easier to code, and it’s pretty accurate for such things as bent tubing, but doesn’t work for cast pipe bends or similar fabricated corners (I can think of a dozen examples).
The comment by @MikeWayzovski, above, is pertinent, because arcs and circles in SketchUp, while calculated like circular curves, are in reality polygons with a fixed number of straight line segments (set in advance of creating the circle or arc). In programs such as AutoCAD, only the graphic representation of circles and arcs are straight line segments, and finding tangents between curves and straight lines, or two curves, is performed accurately. In SketchUp, it’s hit or miss. The straight line segment of a SketchUp curve may “jump” away from the true arc to perform the connection. You can minimize this by using a large number of segments BEFORE creating the arc, but you can’t eliminate this idiosyncrasy of SketchUp.
Until SketchUp implements forced object snaps on demand, an a true tangent join that is based on a calculated arc rather than a polygonal simulation, you may be forced to continue to use whatever work around you find least objectionable.