Dan Coby writes:
I see two red circles and two blue circles. The red circles are the inner and
outer radii. One of the blue circles shows the inner edge of the segments. However
the purpose of the other blue circle is a mystery to me.

What is the purpose of the second blue circle?

The inner blue circle is for the clamping brace. The outer blue circle
is the cutoff for when you switch to the other set of equations - it
identifies the size where you start getting end grain issues, too. When
the OD matches that blue circle, the OD circle is tangent to the edge of
the segment right at the intersection with the adacent segment.