Point/Tanto,L,C
Tangent Point — Line / Circle
Creates a point at the tangent location between a line and a circle. The line must be tangent to the circle.
What It Does
The Point/Tanto,L,C operator creates a point at the exact location where a line is tangent to a circle. The tangent point is the point on the circle circumference where the line touches — the radius at this point is perpendicular to the line.
Prerequisite: The line must already be tangent to the circle. If the line does not touch the circle, no tangent point exists and XyzPilot returns an error.
Syntax
Point/Tanto, L, C, Z
Quick Input
L: [line reference]
C: [circle reference]
Z: 0
Direction Selector
No direction selector is required. The result is uniquely determined by the input geometry.
Worked Examples
Setup:
L0 = Horizontal line at Y=75
C0 = Centre (50, 50), radius 25
Point/Tanto, L0, C0, 0
→ P13 = (50, 75)
[tangent point at top of circle]
Verification:
dist(C0 centre, P13) = dist((50,50),(50,75)) = 25 = radius ✓
Line L0 is perpendicular to radius at P13 ✓
Analytic Rule
Tangent condition: dist(circle centre, line) = radius
Tangent point: perpendicular projection of centre onto line
If line equation: ax + by + c = 0
Tangent point: (cx - a*r/|n|, cy - b*r/|n|)
where n = (a,b) is the line normal vector
Result: Exact analytic tangent point.
FAQ
What if the line is not tangent to the circle?
XyzPilot returns an error. The line must be tangent to the circle for a tangent point to exist. Use Line/P,Tanto,C to create a tangent line first.
How do I create a tangent line first?
Use Line/P,Tanto,C to create a line through a point tangent to a circle, or Line/Parlel,L,Tanto,C to create a parallel tangent line.