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.
Answer
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'.
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