How To Fit 4 Tangent Circles between 2 Radii and Tangent To Lines That Pass Through The Center Of A Circle

[anthony53CX7]

Hello All,

First time posting on this forum. I would like to know if there is a way to fit 4 circles between these radii. The purple radii can not move. The red circles/lines can change. There need to be 4 circles. the red lines need to go through the center of the purple circles. These red lines need to be tangent to the red circles as well. The 4 red circles also need to take up the entire space (Right now I'm off by about 0.005). Please let me know if you need any additional information. Thank you.

[pendean]

Share your DWG file here please.

[anthony53CX7]

Attached the DWG Here

[Brock_Olly]

I don't think there's a way to automatically do this in autocad but I'm sure it can be done with trigonometry though I'm not smart enough for that it seems 

[Brock_Olly]

I asked chatGPT and he struggled quite a bit, had to change prompt around a lot but he might be on to something:

[Washingtonn]

What was your method up to this point?

Can you show your work?

What is an acceptable tolerance?

[anthony53CX7]

Up to now I kept adjusting the radius of the top circle, creating tangent lines from the center of the radii to the top circle, and then used TTT to create the other 3 circles. I was able to get it within ~1/128in. I was hoping to find a way to make it perfect without using geometry/equations.

[Washingtonn]

The black circles are to remain after erasing all other lines....

[anthony53CX7]

Hello,

Thank you for your response. This does get it to be close, but this is not exactly what I was looking for. Thank you for the alternative way of getting the circles close though.

[Washingtonn]

Even using Solver in Excel (though you didn't want to use formulas.....), a small tolerance remains (0.00000097) in the distance between diameters and differences between arcs.  What is the purpose/use?

[anthony53CX7]

I had a project that needed this to be done within a tolerance. I was genuinely curious if it was possible to get the tolerance down to 0. Thank you for the help though!