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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

SelectorPicks
XLargePerpendicular tangent line with largest X tangent point
XSmallPerpendicular tangent line with smallest X tangent point
YLargePerpendicular tangent line with largest Y tangent point
YSmallPerpendicular 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.