Line/Tangent,A
Tangent to Arc at Endpoint
Creates a line tangent to an arc at its start or end point. The tangent direction is perpendicular to the radius at the selected endpoint.
What It Does
The Line/Tangent,A operator creates a line tangent to an arc at either its start or end point. The tangent direction is always exactly perpendicular to the radius at the selected endpoint.
Syntax
Line/Tangent, A1, Start|End
Quick Input
A: [arc reference]
Point: ● Start ○ End
Direction Selector
| Selector | Result |
|---|---|
Start | Tangent line at the arc start point — direction perpendicular to radius at start angle |
End | Tangent line at the arc end point — direction perpendicular to radius at end angle |
Worked Examples
Setup:
A0 = Arc: centre (0,0), r=50, start=0°, end=90° CCW
Start point: (50, 0) [at 0°]
End point: (0, 50) [at 90°]
Line/Tangent, A0, Start
→ L0: through (50,0), direction=90° (vertical)
Radius at 0° points right (+X)
Tangent is perpendicular = vertical
Line/Tangent, A0, End
→ L1: through (0,50), direction=0° (horizontal)
Radius at 90° points up (+Y)
Tangent is perpendicular = horizontal
Analytic Rule
Tangent direction at arc endpoint:
Radius direction at angle A: (cos A, sin A)
Tangent direction: perpendicular = (-sin A, cos A)
For Start: A = start_angle
For End: A = end_angle
Tangent line passes through the endpoint
in the tangent direction.
Result: Exact analytic tangent line.
FAQ
Why is the tangent perpendicular to the radius?
By definition, a tangent to a circle at a point is perpendicular to the radius at that point. This is a fundamental property of circles and arcs.
Can I create a tangent at a point other than start or end?
Use Point/On,A,Atangl to create a point at any angle on the arc, then use Line/P,Atangl to create a tangent line at that point.