Line/Perpto,L(angled),Tanto,C
Perpendicular to Angled Line and Tangent to Circle
Creates a line perpendicular to an angled line and tangent to a circle. Direction selector required.
What It Does
This operator creates a line perpendicular to an angled (non-horizontal, non-vertical) reference line and simultaneously tangent to a circle. The perpendicular direction is exactly -1/slope of the reference line.
Syntax
Line/Perpto, L1(angled), XLarge|XSmall, C1
Quick Input
L: [angled reference line]
Dir: ○ XL ○ XS
C: [circle — tangent to this]
Direction Selector
| Selector | Picks |
|---|---|
XLarge | Perpendicular tangent line with largest X tangent point |
XSmall | Perpendicular tangent line with smallest X tangent point |
Worked Examples
Setup:
L0: slope=1, equation y=x
C0: centre (60,20), radius 15
Perpendicular to L0: slope=-1
Line/Perpto, L0, XSmall, C0
→ L1: slope=-1, tangent to C0, left solution
Line/Perpto, L0, XLarge, C0
→ L2: slope=-1, tangent to C0, right solution
Analytic Rule
Perpendicular slope = -1/slope(L)
Offset line at distance r from circle centre
in perpendicular direction.
Two solutions — direction selector picks one.
Result: Exact analytic perpendicular tangent line.
FAQ
How is the perpendicular direction computed?
For a line with slope m, the perpendicular slope is -1/m. For a horizontal line (m=0), the perpendicular is vertical. For a vertical line, the perpendicular is horizontal.
What selector should I use?
Use XLarge/XSmall when the two solutions differ primarily in X coordinate. For lines at 45°, both selectors work — choose based on which tangent point you want.