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I'm new to Adobe Illustrator and I wanted to accomplish this task. How do I remove the inner lines in my drawings? I tried with all the pathfinders effect but it keeps removing my tangent lines (the lines connecting both my circles).
It works like a charm as I followed the selected's answer guide:
Here it is.
Pathfinder won't find anything with just lines -- it only works with the area that a path is enclosing. You'll want to connect your tangent lines and make them into a solid shape, a rectangle in this case.
Use the white arrow tool to select the right-end anchors of both lines (click on the first, shift-click on the second) and then Object > Path > Join (or Ctrl/Opt + J). Do so again for the two right-end anchors to end up with a rectangle-like shape.
Select this shape and both circles and choose the first Pathfinder option 'Unite'.
There's a script for that, which has the added advantage of giving you perfect connecting tangent lines.
It's called Metaball by the awesome Sato Hiroyuki - you can download it as part of a big bundle of mostly useful Illustrator scripts from his page here.
It turns a selection of circles into singular blobs by following tangent lines. Here's an example from that page - you can also input a value for the curve, and if you input 100, it gives perfectly straight lines like in your example.
Because it creates closed path shapes, you can select the paths it creates along with the circles, use Unite (the first of the Pathfinder window options), and it just works perfectly.
If you're working with tangents, also check out Common Tangents and Tangents From A Point from the same script bundle. Here's two examples from that site:
While most of the answers posted online are almost correct and give visually desired effect, I needed something 100% precise. Check out the references at the end to see animated geometrical construction of tangents.
For starters make sure to disable "Align to Pixel Grid" and "Align New Objects to Pixel Grid" in Transform Pane. You would probably have to zoom in few times to make sure anchors are placed in the intersections (as Illustrator sucks at it big time). Also, if the circles are not nicely aligned to each other, you will probably have to make some additional steps like: duplicate, rotate to horizontal position, draw stuff, rotate back again.
It takes some time and practise to draw tangent. The first part is creating a tangent through a point:
The second part is using the created tangent to make a circle-circle tanget:
Final illustration for above steps:
References (with animations):
I am crazy late in answering this, but this might be of use to somebody anyway.
I make three shapes, two circles and one adjusted square. Note the delightful colours, just to make it clear what shapes I have made:
Select all with the selction tool, then click the shape builder:
Start in the outer half of one of the circles and "pull" over to the other end:
voilà:
