Line/Perpto,L,Tanto,C
Perpendicular to Line and Tangent to Circle
Creates a line perpendicular to an existing line and tangent to a circle. Direction selector required.
What It Does
The Line/Perpto,L,Tanto,C operator creates a line that is simultaneously perpendicular to an existing line and tangent to a circle. Two solutions exist — the direction selector specifies which one.
Syntax
Line/Perpto, L1, XLarge|XSmall|YLarge|YSmall, C1
Quick Input
L: [reference line — perpendicular to this]
Dir: ○ XL ○ XS ● YL ○ YS
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 |
YLarge | Perpendicular tangent line with largest Y tangent point |
YSmall | Perpendicular tangent line with smallest Y tangent point |
Worked Examples
Setup:
L0 = Horizontal line at Y=0
C0 = Centre (50,40), radius 20
Perpendicular to L0 = vertical lines
Tangent to C0: X = 50-20=30 or X = 50+20=70
Line/Perpto, L0, XSmall, C0
→ L1: vertical line X=30 (left tangent)
Line/Perpto, L0, XLarge, C0
→ L2: vertical line X=70 (right tangent)
Analytic Rule
Perpendicular to L constrains direction.
Tangent to C constrains position.
Offset line from L in perpendicular direction
at distance = circle radius from circle centre.
Two solutions exist — one each side of circle.
Result: Exact analytic line.
FAQ
What if the circle is not near the perpendicular direction?
XyzPilot computes the perpendicular direction from L, then finds the two lines in that direction tangent to C. The circle does not need to be near L.
How is this different from Line/Parlel,L,Tanto,C?
Line/Perpto,L,Tanto,C creates a line perpendicular to L. Line/Parlel,L,Tanto,C creates a line parallel to L. Both are tangent to C.