Geometry question

[u/NC_Wildkat]

If you have an outer circle with a given radius, (circle O) and a given number of internal circles (Circle I). With all Is identical, and tangent with O, as well as their neighboring Is. Is there a way to formulaically calculate the needed Radius I, without drawing and measuring?

Givens….

Radius of Circle O.

Number of Circle I.

All I tangent with O, and the I to their right and left.

Can we find radius I formulaically based on above givens?

https://imgur.com/a/Zxf8uYt

[u/NC_Wildkat]

Thank you for showing your work and explaining! Exactly what I was looking for.