I'm trying to match up two lines on a drawing I am doing, without changing the length of either line. There is a perfect set of angles to do so- I just don't know what it each. Is there a built in functionality to do this?

This is what it currently looks like:




1 Answer 1


It's a really simple problem with a simple solution and I doubt that there's a built-in solution.

All you need to do is to draw a circle on each line with its radius equal to the length of the line and its centre on the stationary end of the line.

You will encounter three possible cases:

  1. The circles don't intersect - the lines won't meet
  2. The circles are tangential to each other - the lines will end up co-linear
  3. The circle intersect at to points - two solutions exist.

This may be tedious if you have a lot of lines, but considering the multiple possible solutions, a built-in function will also require you to inspect that the correct solution has been accepted.

Below is an image showing the two-solution case. The red lines are the initial condition and the blue lines are the two possible solutions:

enter image description here

  • 1
    $\begingroup$ There actually is a built in solution. Its called constraints the benefit of that is should your dimensions change it would just find a new solution. This has been the cornerstone of nearly all mechanical 3D engineering since 1980's, while autocad is late to the party its there. It works well and solves nearly any geometric problem you have, quickly an easily. Most solvers also find the closest solution so it minimizes (but does not eliminate) checking. $\endgroup$
    – joojaa
    May 3, 2018 at 12:22
  • $\begingroup$ Yes, I know constraints quite well. That's probably a better solution also, my head was just stuck on the idea of a single command. One thing though, especially for AutoCAD, to ensure that it doesn't mess up your sketch you need to set up a lot of other constraints which can become cumbersome and error prone. $\endgroup$
    – ChP
    May 3, 2018 at 12:44
  • $\begingroup$ Yeah thats why i prefer systems that autoconstain. $\endgroup$
    – joojaa
    May 3, 2018 at 12:45
  • $\begingroup$ To future-proof your sketches, the extra effort with constraints are definitely worth while, but for a quick once-off solution to this specific question I would stick with plain old Euclidean geometry $\endgroup$
    – ChP
    May 3, 2018 at 12:46

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