line tangent to two circles?

Hi All:

I found the "Tangent Arcs" command, but not its linear equivalent. Does anyone know how to create a line that is tangent to two circles?

Better yet, what would be the best strategy for finding the points at which two circles have co-linear direction vectors?

Adam

Replies to This Discussion

Permalink Reply by Daniel Piker on June 14, 2010 at 4:13am

There's probably a simpler way, but here's one geometric approach. (Assuming it is only the exterior tangents you want) :

Permalink Reply by Danny Boyes on June 14, 2010 at 4:57am

Hi Daniel, what exactly are you doing there as the resolution is a bit small for my eyes. Are you using Thales Theorem:

to get the tangent from the centre of one circle and then using its parallel?

Permalink Reply by Daniel Piker on June 14, 2010 at 5:07am

Hi Danny,
Yes, exactly.
The full resolution image is there in my post, just open it in a new tab and delete the"?width=721" bit off the end. (It's an annoyance of Ning that clicking images doesn't automatically open them full size)

Permalink Reply by Danny Boyes on June 14, 2010 at 5:27am

wow, that's what I've learnt today (about ning, anyway)

Permalink Reply by Adam OHern on June 14, 2010 at 7:50am

That's great guys, thanks a lot!

Is there a way to get the interior tangents? It turns out I actually need them too.

Permalink Reply by Daniel Piker on June 14, 2010 at 8:46am

Getting interior tangents works almost the same way, just adding the radii to begin with instead of subtracting.
http://en.wikipedia.org/wiki/Tangent_lines_to_circles#Geometrical_c...

Permalink Reply by Ben Sitler on June 14, 2010 at 11:13am

Adam,

Another option is to use tangent arcs and set the radius to a very large number. Then extract the arc/circle intersections and draw the respective tangent lines. Of course this is just an approximation, albeit one with negligible tolerance.

Ben

Attachments:

tangent lines.ghx, 103 KB

Permalink Reply by Adam OHern on June 14, 2010 at 11:20am

Thanks Ben. The thought occurred to me, but my anal-retentiveness makes it hard for me to do things like that without breaking into hives. :)

Thanks for the template!

Permalink Reply by Vicente Soler on June 14, 2010 at 12:12pm

When everything else fails (or you are too lazy too look up the appropriate theorem) you can always replace your brain with your CPU and make your computer "brute-force" a solution using Galapagos.

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