Circle/Tanto,C,C,R
Circle Tangent to Two Circles
Creates a circle tangent to two existing circles with a specified radius. Selector and IN/OUT required.
What It Does
The Circle/Tanto,C,C,R operator creates a circle of specified radius simultaneously tangent to two existing circles.
Syntax
Circle/Tanto, C1, C2, R, XLarge|XSmall|YLarge|YSmall, IN|OUT
Quick Input
C: [first circle]
C2: [second circle]
R: [radius]
Dir: ○ XL ○ XS ● YL ○ YS
Tan: ● OUT ○ IN
Direction Selector
| Selector | Meaning |
|---|---|
OUT | Externally tangent to both circles |
IN | Internally tangent to one or both |
Worked Examples
C0=centre(0,0) r=20, C1=centre(80,0) r=20, R=30
Circle/Tanto, C0, C1, R=30, YLarge, OUT
→ C2: externally tangent to both, upper solution
dist(C2,C0)=50=30+20 ✓ dist(C2,C1)=50=30+20 ✓
Analytic Rule
External: dist(new centre, C centre) = R + r_C
Internal: dist(new centre, C centre) = |R - r_C|
Solve circle-circle intersection for new centre.
Result: Exact analytic circle.
FAQ
How many solutions?
Up to eight — four tangency type combinations, each with up to two solutions.
What is the Apollonius problem?
Finding a circle tangent to three given circles. Circle/Tanto,C,C,R solves the two-circle case with specified radius.