Circle/From,P1,P2 — Circle from Two Points

What It Does

The Circle/From,P1,P2 operator creates a circle where:

Centre = P1 (the first point)
Radius = dist(P1, P2) — the distance from P1 to P2

This is equivalent to Circle/Centre,P1,R where R is computed automatically from the distance between the two points. It is useful when you know the centre and a point on the circumference, but not the explicit radius value.

Product Tier: Circles are persistent product entities tracked by the dependency system.

Syntax

Circle/From, P1, P2

Parameter	Description	Required
`P1`	Centre point reference	✓ Yes
`P2`	Point on the circumference — defines the radius	✓ Yes

Quick Input

P:  [centre point reference]
P2: [circumference point reference]

Worked Examples

Example 1:
  P0 = (50, 50)  [centre]
  P1 = (80, 50)  [point on circumference]
  dist(P0, P1) = 30

  Circle/From, P0, P1
  → C0: centre=(50,50), radius=30

Example 2:
  P0 = (0, 0)   [centre at origin]
  P1 = (0, 40)  [point directly above]
  dist(P0, P1) = 40

  Circle/From, P0, P1
  → C1: centre=(0,0), radius=40

Example 3 — diagonal:
  P0 = (10, 10)
  P1 = (40, 50)
  dist = sqrt((40-10)^2 + (50-10)^2) = sqrt(900+1600) = 50

  Circle/From, P0, P1
  → C2: centre=(10,10), radius=50

Analytic Rule

Centre: (cx, cy) = (P1.x, P1.y)
Radius: r = sqrt((P2.x - P1.x)^2 + (P2.y - P1.y)^2)

Circle equation: (x - cx)^2 + (y - cy)^2 = r^2

Result: Exact analytic circle. No selector needed.

FAQ

What is the difference between Circle/From,P1,P2 and Circle/Centre,R?

Circle/Centre,R requires you to specify the radius as an explicit numeric value. Circle/From,P1,P2 computes the radius automatically from the distance between the two points — useful when you know a point on the circumference but not the exact radius.

Does P2 have to be on the circumference?

Yes. P2 defines the radius — it is the point on the circumference. The circle passes through P2 exactly.

Related Operators

Circle/Centre,R

Circle from Two Points