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Radius of a circle passing through 3 points

c-ito

I want a script to find the radius of a circle that passes through three points

For example
A: (1,2)
B: (3,4)
C: (5,6)
Is it possible to easily find the radius of a circle passing through ABC?

Accepted answers

Craige_Hales

Sure, draw a line from {xc,yc} (the center) to any point on the circle. Three good candidates are {ax,ay}, {bx,by} and {cx,cy} . A diameter would be slightly harder, but you could find the point opposite A, through the center, at {CX + (CX-AX), CY + (CY-AY)}. You also know the radius is

Sqrt( (xc - ax) ^ 2 + (yc - ay) ^ 2 )

(using the center point and point A) so you could find other points as well, using cx + r*cos( a ), cy + r*sin(a), for various angles in radians.

All comments

Craige_Hales

Circle through three points

Mark_Bailey

And I like you example of a circle!

Screen Shot 2020-12-24 at 8.42.01 AM.png

Craige_Hales

I'm degenerate!

Good point (!) , you'll want to watch out for edge cases.

c-ito

Thank you SCL for illustrating the circle.
It helped me a lot!

Is it possible to show the radius?

Craige_Hales

Sqrt( (xc - ax) ^ 2 + (yc - ay) ^ 2 )

(using the center point and point A) so you could find other points as well, using cx + r*cos( a ), cy + r*sin(a), for various angles in radians.