Line/C,Atangl
Tangent to Circle at Angle
Creates a tangent line to a circle at a given angle. Direction selector required — two solutions exist.
What It Does
The Line/C,Atangl operator creates a line tangent to a circle at a specified angle (line direction). Two tangent lines at any given angle exist — one on each side of the circle. The direction selector specifies which one.
Syntax
Line/XLarge|XSmall|YLarge|YSmall, C, Atangl, A
Quick Input
Dir: ○ XL ○ XS ● YL ○ YS
C: [circle reference]
Angle: [line direction angle in degrees]
Direction Selector
| Selector | Picks |
|---|---|
XLarge | Tangent line whose tangent point has the largest X coordinate |
XSmall | Tangent line whose tangent point has the smallest X coordinate |
YLarge | Tangent line whose tangent point has the largest Y coordinate |
YSmall | Tangent line whose tangent point has the smallest Y coordinate |
Worked Examples
Setup:
C0 = Centre (50,50), radius 30
Angle = 30° (line direction)
Line/XLarge, C0, Atangl, 30
→ L0: tangent to C0 at 30°, right-side tangent point
Line/XSmall, C0, Atangl, 30
→ L1: tangent to C0 at 30°, left-side tangent point
Analytic Rule
Tangent point at angle A on circle:
Tangent direction: (cos A, sin A)
Normal direction: (-sin A, cos A)
Two tangent points: centre ± r * normal
Two tangent lines exist — one each side.
Direction selector picks which tangent point to use.
Result: Exact analytic tangent line.
FAQ
How is the angle measured?
The angle specifies the direction of the tangent line, measured from the positive X axis counterclockwise. 0° = horizontal line. 90° = vertical line.
What is the difference between this and Line/P,Tanto,C?
Line/C,Atangl creates a tangent at a specified angle (direction). Line/P,Tanto,C creates a tangent through a specified point.