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Point/Tanto,C,C

Tangent Point — Circle / Circle

Creates a point at the tangent location between two circles. The circles must be tangent to each other.

What It Does

The Point/Tanto,C,C operator creates a point at the exact location where two circles are tangent to each other. Two circles can be tangent externally (touching on the outside) or internally (one inside the other, touching at one point).

Prerequisite: The circles must be tangent. External tangency: dist(centres) = r1 + r2. Internal tangency: dist(centres) = |r1 - r2|.

Syntax

Point/Tanto, C1, C2, Z

Quick Input

C: [first circle reference] C2: [second circle reference] Z: 0

Direction Selector

No direction selector is required. The result is uniquely determined by the input geometry.

Worked Examples

Example 1 — External tangency: C0 = Centre (50, 50), radius 25 C1 = Centre (100, 50), radius 25 dist(centres) = 50 = 25 + 25 ✓ (externally tangent) Point/Tanto, C0, C1, 0 → P14 = (75, 50) [midpoint between centres] Example 2 — Internal tangency: C0 = Centre (0, 0), radius 50 C1 = Centre (20, 0), radius 30 dist(centres) = 20 = 50 - 30 ✓ (internally tangent) Point/Tanto, C0, C1, 0 → P15 = (50, 0) [on the larger circle, in direction of C1]

Analytic Rule

External tangency: dist(c1, c2) = r1 + r2 Tangent point lies on the line between centres at distance r1 from c1 (or r2 from c2) Internal tangency: dist(c1, c2) = |r1 - r2| Tangent point lies on the line between centres at distance r1 from c1 in the direction of c2 Result: Exact analytic tangent point.

FAQ

What if the circles are not tangent?

XyzPilot returns an error. The circles must be exactly tangent for a tangent point to exist. Check that dist(centres) equals r1+r2 (external) or |r1-r2| (internal).

How do I know if circles are externally or internally tangent?

External: the circles touch on the outside, dist(centres) = r1 + r2. Internal: one circle is inside the other and they touch at one point, dist(centres) = |r1 - r2|.