Revit Adaptive Component Circle from 3 tangents

[yskert.schindel]

Hi all,

please excuse that this ist not a Dynamo topic, but the Autodesk Revit forum seems to be of no help.

I’m working on an Adaptive Component Family where I want to create an arch that is tangent to 2 lines and one circle.

This is a rough sketch of what it should look like in the end:

To achieve this I think I have to use the arch from 3 points. All those 3 points are the exact tangent points on the other circle and the two reference lines.

The following geometric problem arises:

The black circle and lines are given. The black points and dimensions are known.

I want to construct the red circle trough all 3 green points. To do this in Revit I think i need to know all blue dimension values.

I tried searching google, but this does not seem to be a standard problem.

Hope some of you math-geniuses may be able to help me

[yskert.schindel]

I think I found a name to the problem:

Special cases of Apollonius' problem | Type 8: One circle, two lines

[jacob.small]

Does it have to be an adaptive component?

[yskert.schindel]

Not absolutely nessecary, but it would preferrable.
There are 9 other families in the system and, if possible, I’d like to stay with the same method for all of them. This way I can reuse common sub-families easier.

Here is a screenshot of the whole system:
(I am talking about the corner element)