Circle/Tan/To/A,L
Circle Tangent to Arc and Line
Creates a circle of specified radius tangent to both an arc and a line. Direction selector and IN/OUT required.
What It Does
The Circle/Tan/To/A,L operator creates a circle of specified radius that is simultaneously tangent to an existing arc and an existing line. Multiple solutions exist — the direction selector and IN/OUT tangency type specify which one.
Syntax
Circle/Tan/To/A,L, A, L, R, XLarge|XSmall|YLarge|YSmall, IN|OUT
Quick Input
L: 0
A: 0
R: 5
IN/OUT: OUT IN
Dir: XL XS YL YS
Direction Selector
| Selector | Meaning |
|---|---|
OUT | New circle externally tangent to the arc |
IN | New circle internally tangent to the arc |
XLarge/XSmall/YLarge/YSmall | Selects which remaining solution to use |
Worked Examples
Setup:
A0 = Arc: centre(50,30), radius 15, 0 to 180 CCW
L0 = Horizontal line at Y=0
R = 10
Circle/Tan/To/A,L, A0, L0, R=10, YLarge, OUT
→ C0: tangent to L0 above, externally tangent to A0
dist(C0 centre, L0) = 10 = R
dist(C0 centre, A0 centre) = 10+15 = 25
Analytic Rule
New circle tangent to line L: dist(centre, L) = R
New circle externally tangent to arc A: dist(centres) = R + A.radius
New circle internally tangent to arc A: dist(centres) = |R - A.radius|
Solve simultaneously for new circle centre.
Multiple solutions — selectors pick which one.
Result: Exact analytic circle.
FAQ
How is this different from Circle/Tanto,L,P?
Circle/Tanto,L,P is tangent to a line and a full circle. Circle/Tan/To/A,L is tangent to a line and an arc — the arc constraint respects the arc sweep angles.
How many solutions can exist?
Up to four solutions may exist for a given R, A, and L combination. The direction selector and IN/OUT narrow it to one.