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Take a look on the image. I have a line with two segments (on the left). How to make smooth connection between them keeping one segment untouched (right side)? I know two methods but they are not so easy. I need a method that takes one or two actions.
Update: It seems we need a plugin for this, as there is no good answer.
Unless I've missed something, there's an easier way that still keeps the line 100% perfectly straight.
Three simple steps, needing just two clicks and at most three common keyboard shortcuts:
p) to select the path end point closest to the segment you want to stay straight. This makes sure the direction of the path is pointing towards the segment you want to keep straight. So in your example, if you drew it left-to-right, use the pen tool to select the left hand end point - which (invisibly, unless like in my screenshot example below you have arrowheads or a brush on the path stroke) turns the direction of the path around. You don't need to do anything else with the pen tool, just select the end point then move on to step two.
cmd-U, or under the View menu)shift-c), drag on the corner keeping your cursor over the straight line segment. The smart guides will help you stay precisely on the line, keeping that part perfectly straight. 
Tip: Make sure the only visible piece of bright green Smart Guide noise is a tiny green cross telling you you're perfectly over the line (as in the screenshot above). Illustrator smart guides love nothing more than matching your points up against completely random-seeming unexpected things.
The significance of step one is, if the path was other wrong way round, you'd be controlling the wrong handle, so either the path would bend the wrong way, or your cursor would be opposite to the straight path so you wouldn't be able to use the smart guides to stay perfectly on course.
Note how the green X above (cursor position) is in the exact equivalent position to in the previous image - but with the path the other way round, the result is very different.
If you want, you can then tidy up and get rid of that redundant extra handle that is sitting on top of the straight path segment. You don't need to, but it might make the shape easier to work with, depending on what you're trying to do.
To do so, use the white arrow (direct selection tool, A), and drag that handle back onto the corner . The smart guides will help you drop it precisely on the corner.
The other handle might go crazy when you're near the corner, but when you have it precisely on the corner, it'll calm down. Alternatively, holding down alt while dragging one handle tells the other handle to just stay where it is.
There are third-party plug ins which make this a single click-drag operation, but Illustrator doesn't provide any comparable method itself.
I would suggest the following method:
Convert Anchor Point Tool, click on your corner point and drag along the pasted segment letting the handle stick to the pasted segment - this will ensure the smoothness of the connection.I just copied/extended the line and moved it to the top anchor point then converted this into a path. Now you are able to ALT+drag with the path tool and use the created guide as a constraint
shift-c-click/drag (if you've got smart guides on and the pen tool active from having finished drawing - and you only need the first click some of the time). There might be something in Vectorscribe that is only one click, but what do you need to do that can't be done without plugins? You also never said what the two methods you knew were.