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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

SelectorMeaning
OUTExternally tangent to both circles
INInternally 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.