Many times my students fight with constructing Arcs and Circles with given constraints.
This is one of those little challenges - Do you have similar ones - please share them here.

The trapped Arc

Given:

a horizontal Line.

At the start of the Line a tangential Circle with R25 (D50)
Searched:
An Arc with R5 (green) that is tangent to the Circle and perpendicular to the line.
(I will post 2 solutions later, if others don’t post them earlier)

looking forward to see your solutions - and other challenges. kind regards - tom

Seems to me that there are an infinite number of solutions depending on what the phrase “At the start of the Line a Circle” means.
Did you mean the center of the circle is perpendicular to the line or will any 25 unit circle that touches the end of the line do?

i think a quicker trig solution is
the distance of the d5 center from the line-circle intersection is given by: (d25+d5) * sin ( arccos( d25 / (d25+d5) )

1 fixed Circle + 2 constrained Circles along Lines.
Big Circle with thickness tangent to the 3 circles.

I thought it was a challenge until I modelled it in Rhino…
Anyway, it would be interesting to see it with Rhino Constraints feature.
cc @Joshua_Kennedy.