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Point/Tanto,C,A

Tangent Point — Circle / Arc

Creates a point at the tangent location between a circle and an arc. Direction defaults to external unless internal is selected.

What It Does

The Point/Tanto,C,A operator creates a point at the exact location where a circle and an arc are tangent to each other. The tangency direction defaults to external unless internal is selected in the Quick Input panel.

Canvas Preview: The transient preview may show the point in the wrong position while the tangency direction is being selected. Always verify the final position after committing.

Syntax

Point/Tanto, C, A, Z

Quick Input

C: [circle reference] A: [arc reference] Z: 0 Label: (optional) Dir: ● External ○ Internal

Direction Selector

The tangency direction selector determines whether the circle and arc touch on the outside (external) or inside (internal):

DirectionMeaning
External (default)Circle and arc touch on the outside — the tangent point is between them
InternalOne entity is inside the other — they touch at one point on the inner boundary
Important: The tangency is always external until Internal is explicitly selected in the Quick Input panel.

Worked Examples

Setup: C0 = Circle: centre (0,0), radius 20 A0 = Arc: centre (50,0), radius 20, 90° to 270° CCW External tangency: dist(centres) = 50 = 20 + 20 + 10... check geometry Point/Tanto, C0, A0, 0 [External] → P0 = tangent point on outer boundary Point/Tanto, C0, A0, 0 [Internal] → P1 = tangent point on inner boundary

Analytic Rule

Tangency condition same as circle-circle: External: dist(centres) = r_circle + r_arc Internal: dist(centres) = |r_circle - r_arc| Tangent point: on line between centres at distance r_circle from circle centre Result: Exact analytic tangent point.

FAQ

What is the difference between internal and external tangency?

External tangency: the circle and arc touch on the outside, with the tangent point between them. Internal tangency: one is inside the other, touching at one point on the inner boundary.

Why does the preview show the wrong point?

The transient preview updates as you change the tangency direction. The point shown before you commit may not be the final result. Always verify after committing.