Share your Arc / Circle construction challenges

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


  • a horizontal Line.
  • At the start of the Line a tangential Circle with R25 (D50)
    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


I’d do this:
trapped_arc.3dm (162.1 KB)


As for other arc/circle issues: you should be able to find many here


… great - different to mine.

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?

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  • Offset circle 5 to the outside
  • Circle r5 at the intersection of the line and the offset
  • Trim what isn’t necessary (for me the fastest)

Or if you really want to draw the arc directly…

  • Arc center, start, end
  • Pick the intersection of the offset and line as center
  • With Cen Osnap, hover over the circle so center snap is active, then Tab to set direction lock
  • Come back to the r25 circle and pick the start point
  • Snap to the line to finish
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This one from the 4th post is interesting:

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This is my solution:

  • Circle via 2 pts to set the 5mm rad
  • Line tangent to R25 circle and intersecting with center of R5 circle
  • Rotate both circles such that the smaller circle’s center intersects with the horizontal line

Otherwise, I would have just used Pascal’s MoveToTangent script but it throws an error:



Here’s a variable GH solution based on what I posted above… (15.7 KB)


ok here is the collection of posted approaches - and 2 more:

draw dislocated and move

construct with mirror

construct with D30 or _offset D5

(posted by @Gijs and described by @Helvetosaur

draw dislocated and rotate

@vcruzdesigns approach

(@jim updated the initial description - sorry for being imprecise, the circle is tangent to the horizontal line)

Circle_Challenge_01_trappedArc.3dm (1.7 MB)

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i like the offset d5 version, and it was among the first coming to mind as i saw your problem statement.

but there’s even the trigonometric version. SSA triangle, with S1 = 25, S2 = 25+5, A = pi/2

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.