Arc tangent to curves problem

Hi All ,
I am trying to create an ARC tangent to 3 curves but I can’t seem to get it like in Rhino .
it always creates it on the inside of the 2 circles . but I need it on the outside of the 2 circles .
I internalized the curves like I want them to be .
Please Help .
Thank you Arc tangent to 3 curves Problem.gh (9.2 KB)

not 100%, but getting closer… maybe it helps!

Arc tangent to 3 curves Problem_re.gh (17.9 KB)

Hi Amir ,
Your definition is interesting ,but it still is not tangent to the circles .
Thank you though .
Hopefully we will get an answer

Hi Yves! I’m having a crack at it. What are your constraints? How “adaptable” should that arc be?

Hi Pietro
The arc can basically be a circle , but I want the 2 circles to be on the inside of the large circle .
The 2 Circles will move diagonally and change size , but they will never go past the straight curve and they will never change sides on X and Y . The size of the large Circle should automatically adapt to the small circle changes and stay tangent . I hope it makes sense .
Thanks for looking at thisArc tangent to 3 curves Problem V2.gh (9.3 KB)

It does! As a matter of fact, turns out we’re not the first ones to try and crack this problem… maybe it’s the first time that it is done in Grasshopper, though. I found out that this particular problem is the Circle-Circle-Line case of the Problem of Apollonius, so you might want to read up a bit about it… I’ll post anything I can come up with!

Here’s the only other occurrence I found, a post by @maje90!

Here instead I found some geometrical constructions but still haven’t managed to replicate them in Grasshopper.

http://mathafou.free.fr/pbg_en/sol136.html

Thank you Pietro ,
I’ll continue to work on it .

Lol, yes, I was already trying that way, @Pietro_Pedone
Unluckly i’m in a rush, i give you an incomplete work.
2 circles and a line can have many cases, in your specific case the 2 circles have the same exact radius, and that is a problem.

Have a look, i’ll continue it this evening.

incomplete.gh (23.1 KB)

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Hi Riccardo ,
Thank you so much.
That is exactly what I needed . I don’t even understand how you came up with this , but I will try to .
I have a lot of studying to do .
Thanks again