Circle/3P
Circle Through Three Points
Creates a circle passing through three existing point references. No selector needed.
What It Does
The Circle/3P operator creates a circle passing through three existing point references. Three non-collinear points uniquely determine a circle.
Non-collinear required: The three points must not be on the same line.
Syntax
Circle/3P, P1, P2, P3
Quick Input
P: [first point]
P2: [second point]
P3: [third point]
Direction Selector
No direction selector required. The result is uniquely determined by the input geometry.
Worked Examples
P0=(0,0), P1=(100,0), P2=(50,60)
Circle/3P, P0, P1, P2
→ C0: circumscribed circle through all three points
Centre and radius computed analytically
Analytic Rule
Solve three circle equations simultaneously.
Subtract pairs to get two linear equations for centre.
Solve for (cx,cy), then r = dist(centre, P0).
Result: Exact circumscribed circle.
FAQ
What if the three points are collinear?
XyzPilot returns an error — no circle passes through collinear points.
Is this the circumscribed circle?
Yes. This is the circumcircle of the triangle formed by the three points.