How can I get this point?

[spawn]

Hi everybody.

I know TIG developed an extension called True Tangents, but I wasn’t able to get this.

• The center has to be situated in line called B.
• The circle has to touch A,C and D.

It would be something like this:

question.skp (17.2 KB)

I almost forget to thank in advance

[TIG]

With my TrueTangents toolset you can get a cpoint at the intersection of arcs A and C, and much more…

SketchUp Plugins | PluginStore | SketchUcation

This intersection-point will NOT necessarily fall on line B.
You can determine the intersection of A & C, or A & B, or C & B.
BUT not all three at once unless they are coincidental by accident !
So find the intersection of something important to you [like A & C] and the create the line through that, which approximates to B…

[sdmitch]

By my calculation, the radius of the circle through D and tangent to A and C should be 3.1066".

The intersection of A and C is 3.1292" from D.

[slbaumgartner]

I agree with @sdmitch. The formula I came up with is

r = (D^2+H^2-R^2)/(2(H-R))

Where
D is the distance from line B to the arc centers
H is the distance from the line of arc centers to point B
R is the radius of the arcs

Edit: whoops you labeled the point I called B as D! I should have used some other symbol for what I called D! Otherwise the formula is correct.

[spawn]

Thank you guys for your answers and the formula, it will be useful but it looks hard I mean it requires to use the calculator (at least for me)

Isn’t there any calculator built-in on sketchup, right?
I will make some tests with the formula.

TIG, about the extension … I still don’t get how to use it to get the point, I mean … am I using it on the right way?

[spawn]

slbaumgartner

Do I have to change D by B in your formula? or it’s corrected after your editing?

[slbaumgartner]

No need to modify the formula if you read it right:

D is the distance from the arc centers to line B

H is the distance from the line of centers to the point you labeled “D”

[spawn]

Thank you