The fastest way is to use a plug-in. I would get the outer shape by intersecting the four large circles, and then use the Dynamic Corners tool (part of the VectorScribe plug-in) to round the four corners to the small radius. Dynamic Corners can round any corner, even those created from curved beziers.
Total time to create is about 45 seconds.
You may do as DF says, with the alternative option of using the free Round Any Corner script available here:
Some of the other scripts, such as the Common Tangents, may be convenient for other tasks.
Unfortunately, the script suffers from the same problems that the Adobe "Round Corners" effect does:
1) Except for straight-line, right-angle intersections, the corners do not actually have the specified radius. The more acute the angle of the corner, the smaller the radius. So getting the radius close to what you really want is lots of guessing and undoing.
2) Again, except for straight-line, right-angle intersections, the corners are not sections of circles, but more parabolic.
this is easy to do in illy as is,
1. Draw a rectangle (the size of the "inside track") as desired
2. Add 4 anchor points (where i have set the guides)
3. Select the two "horizontal middle" anchors press E (free transform) hold option and drag away from shape to get this:
4. do same to these 2 anchors:
5. Select shape, and apply corner effect.. set radius...
It would be nice to know what would be your approach to such a task.
As you can see from the replies so far, it depends upon the strictness of the geometric requirements. For example, Grant's (Post 6) suggestion does not match the shape of your original. That may be all you're after. That is, if the requirement is for just an "eyeballed" shape, there are several ways to achieve a similar shape. A very quick one would be:
1. Rounded Rectangle Tool: Draw a rounded rectangle.
2. Apply Effect>Warp>Inflate, or two iterations of Effect>Warp>Bulge.
3. Object>Expand Appearance.
The result will be accurately symmetrical and may work just fine for the intended purpose. But the corner arcs may not actually be circular. If you need geometric accuracy (all circular arcs joined with perfect tangency), it can be done in Illustrator, but you have to take the time to deliberately construct the geometry as a workaround for the absense of good geometric construction features in the interace. Your third screenshot is a start, but it is not necessary to construct all four corners. You just need to construct tangency between three different radii (the radius for the top/bottom arcs, the corner arcs, and the side arcs.) Once you have created one quadrant of the shape, the rest can be added with two reflections. For example:
1. Ellipse Tool: Click. Specify a height and width equal to the desired diameter of the corner arcs.
2. Line Tool: Draw a vertical line upward starting by snapping to the cirlcle's center and dragging far enough to cross the circle. (It will intersect the circle at its topmost anchorPoint.)
3. Rotate the line about the circle's center a few degrees counterclockwise.
4. Duplicate the line. Rotate it about the center point to fewer degrees short of horizontal.
5. Select the upper left segment of the circle. Copy. Paste In Front. Delete the circle, leaving just the upper left 90° arc.
6. Scissor: Cut the arc where the two lines intersect it. You now have three tangent circular arcs. The top arc's right end is tangent to 0°. The bottom arc's bottom end is tangent to 90°.
7. Proportionally scale the top arc about its left endpoint. (Tangency between the two arcs is maintained as you scale, because you are scaling about the point of tangency. No matter how much you scale, the other end of the arc will still be tangent to 0°.)
8. Proportionally scale the bottom arc about its top endpoint.
9. Join the three arcs. You now have one quadrant of your figure.
10, Vertically reflect a copy about the rightmost endpoint. Join the two paths. Horizontally reflect a copy about a bottom endpoint. Join the two paths.
Day's (Post 3) comments state the crux of the matter: Illustrator's inteface just doesn't provide things like tangency snaps, as do other drawing programs. If it's a recurring need, the geometry can be automated in script, but that's a far cry from a proper tangency feature in the interface, which is rightly expected in a market-dominating (over-rated and overpriced) general-purpose 2D Bezier drawing program.
Nowadays, 2D CAD-like geometry is pretty ordinary and should be standard fare in any decent drawing program marketed as ostensibly "professional." Illustrator in particular has always been very weak in that regard. Too many of its features are designed to favor a loosey-goosey, artsy-tartsy "eyeballed" approach, without also providing for straightforward numerical/geometric construction. Its hideous Round Corners Effect and Arc tool are prime examples.
as Jet has mentioned, many ways to skin a cat. I believe the OP requires workflow tips, based on his "finished" shape (which is not radius perfect), I have offered him a tip to accomplish a similar shape with minimum effort, and a technique that he can use in future. Calculating geometry to determine radius, ie: if he wants the corner radius as per the 4 small circles seen in his screen shot: and the circles are 25mm butt joined, then he needs the rectangle t be 50mm high. the radius he needs to apply is 12.5 mm... math calculations is also helpful for the other steps.
or he can go the loong way around as per his post, but he needs to learn about aligning techniques..
1. draw your big circles, and 1 small corner circle
2. grab one small circle anchor and snap to the green circle's anchor
3. with the red circle selected grab the Rotation Tool and click on the green circle's center (where the x is)
4. drag the red circle, at this point it will rotate inside the green circle.
4. drop the red circle close to where you want it and zoom in as fas as you can
5. grab it again near the point where you "see" it should snap
6. press Control while dragging, so it snaps to the path.
Thank you all for replies.
So, I have tried the way suggested in the post above.
Here are the screenshots:
I used CTRL+Y to be as accurare as possible. Zoomed in to the maximum level. Looks like it's perfect.
The result after hitting the Divide button in the Pathfinder panel.
So the tiny triangular shape that had to be isolated by the circle was not chopped off. Funny and sad at the same time.
Type design requires high accuracy, but I guess it is very hard to find the shape intersections optically. I wonder why Illustrator has not offered this function yet.
Take a look at the some old sketches from 1912:
ok, pathfinders did not work, try
1. selecting all and using the Paint Bucket Tool, paint all corners, use different color
2. Flatten Transparency
3. Grab the Shape Builder Tool, and move your mouse over the corner piece. Notice the corner will get shaded.
4. Alt+Click on it to remove.
5. then Pathfinder Unite, will give you one shape....damn, too many steps.