Grasshopper Sangaku

Well, it’s not a “real” problem, just my curiosity to find another solution :wink:
As far as I know, a regular sangaku should be solved using algebraic or trigonometry means only. So, my solutions for these two sangakus rely solemnly on calculations and they are well documented. There are links to some sample sites in the definitions.
Now, I can see only one problem I can’t handle with constructive geometry: how to find a centre of a circle tangent to another three circles? Surely, Rhino and Grasshopper gives a tool for constructing one, but how to construct its centre?

So, here I am with sangaku no 1:

And no 2:

I have tried to use as many constructions as possible, just to avoid “calculating”, with minimum input (basically just a point). At the definitions you can find red groups, and these could be changed / improved.

It’s not a request, nor challenge, I just would like to see another approach, if you find the problem interesting. (161.5 KB) (212.4 KB)

Cheers, Jaro