There's a cludgy workaround way I know of to get exact smooth curve joins like that in Illustrator (below).
If you'd rather simply make lots of approximately (not precisely or consistently) smoothed joins check out the Join Reasonably script, co-incidentally discussed on this similar looking question.
So here's my slightly long-winded but precise method (works in CS5).
- Create a 3rd two-point line with the pen tool. The shape and location of this path don't matter, but, hold down and drag slightly on both the first and second clicks so both ends have anchors. Select this path (
V black arrow) and sent it to back (
- With Smart Guides on (
Crtl/Cmd-U), drag one end (using the
A white arrow, ) of the line to exactly overlap one of the other paths' open end points where you want one join to be.
- Select the pair of overlapping points (drag a box around them with the white arrow
A), and join overlapping anchor points (
[Cmd/Ctrl]+Shift+[Opt/Alt]+J). Select 'Smooth' from the popup menu.
- Repeat 2 and 3 for the other pair.
If it doesn't seem to work, double check that the overlapping points in the actual join have anchors. If the ends of the original shapes don't have anchors, add some using the V-shaped tool (
crtl-c), dragging off the point very slightly in the direction the line is going. Also double check that they perfectly overlap.
If the wrong path section changes shape with the smooth join, you might have forgotten to send the new path to back before starting (also make sure it's not on a higher layer than the other paths).
It's not a simple method for what ideally would be a simple task, but it works.