Line/P,Tanto,C
Tangent Line from Point to Circle
Creates a line through a point tangent to a circle. Direction selector required — two tangent lines exist.
What It Does
The Line/P,Tanto,C operator creates a line passing through a point P that is tangent to a circle C. Two tangent lines exist from any external point to a circle — the direction selector specifies which one.
External point required: The point must be outside the circle. If P is inside the circle, no tangent line exists.
Syntax
Line/P1, XLarge|XSmall|YLarge|YSmall, Tanto, C1
Quick Input
P: [external point reference]
Dir: ○ XL ○ XS ● YL ○ YS
C: [circle reference]
Direction Selector
| Selector | Picks |
|---|---|
YLarge | Tangent line whose tangent point has the largest Y coordinate |
YSmall | Tangent line whose tangent point has the smallest Y coordinate |
XLarge | Tangent line whose tangent point has the largest X coordinate |
XSmall | Tangent line whose tangent point has the smallest X coordinate |
Worked Examples
Setup:
C0 = Centre (0,0), radius 20
P0 = (50, 0) [external point]
Tangent length = sqrt(50² - 20²) = sqrt(2100) ≈ 45.826
Line/P0, YLarge, Tanto, C0
→ L0: upper tangent line
Tangent point: upper side of C0
Line/P0, YSmall, Tanto, C0
→ L1: lower tangent line
Tangent point: lower side of C0
Analytic Rule
Tangent condition: dist(circle centre, line) = radius
Tangent length from P to tangent point:
t = sqrt(dist(P, centre)² - r²)
Two tangent lines exist — one each side.
Direction selector picks which tangent point to use.
Result: Exact analytic tangent line.
FAQ
What if the point is inside the circle?
No tangent line exists from a point inside a circle. XyzPilot returns an error. The point must be outside the circle.
How do I create a tangent line between two circles?
Use Line/Tanto,C,C — the common tangent to two circles operator.