## Calculate Center and Radius of Circle from 3 points on it

find center of circle with 3 points calculator
center of circle passing through 3 points
calculate radius from 3 points excel
equation of circle passing through 3 points in 3d
write the general equation for the circle that passes through the points (1, 1, 1, 3 and 9, 2)
find the equation of the circle passing through the points (0), (2,3 0 and (3 2))
write the general equation for the circle that passes through the points (1, 2 4, 2,3, 4)
calculate point on circle

Could somebody please show code which would do this quickly? Assume we get three points p1, p2, p3 in left-->right order. Thus, the solution should also check whether or not the circle is valid, ie (p1, p2, p3) are counter-clockwise.

To calculate the circle parameters, have a look at:

http://paulbourke.net/geometry/circlesphere/ Look for "Equation of a Circle from 3 Points (2 dimensions)"

to determine orientation, you can use the polygon area formula:

http://paulbourke.net/geometry/polygonmesh/ Look for "Calculating the area and centroid of a polygon"

Please tell me if you need this in an specific programming language.

Calculate Center and Radius of Circle from 3 points on it, Center point (x, y) and the radius of a circle passing through 3 points (x1, y1) (x2, y2) Find the equation of a circle that passes through the points (−3 , 4) , (4 , 5)  Circle Radius = Square Root (.6558) Circle Radius = .8098. As you can see, calculating a circle center based on 3 known points can be a bit complicated. Fortunately there is an easy way to calculate the circle center and circle radius.

Circle defined by 3 points, Finding the Center of a Circle from Three Points: How can I find the coordinates of the center of a circle, given the coordinates of three points on its circumference​  Connect any two points on the circle and you have a chord. The perpendicular bisector of a chord must pass through the center. The intersection of the bisectors of two chords will be the center.

Here is a short function (Swift language) with only a single if.

```enum Result {
case invalid
}

func circleTouching3Points(a: CGPoint, b: CGPoint, c: CGPoint) -> Result {
let d1 = CGPoint(x: b.y - a.y, y: a.x - b.x)
let d2 = CGPoint(x: c.y - a.y, y: a.x - c.x)
let k: CGFloat = d2.x * d1.y - d2.y * d1.x
guard k < -0.00001 || k > 0.00001 else {
return Result.invalid
}
let s1 = CGPoint(x: (a.x + b.x) / 2, y: (a.y + b.y) / 2)
let s2 = CGPoint(x: (a.x + c.x) / 2, y: (a.y + c.y) / 2)
let l: CGFloat = d1.x * (s2.y - s1.y) - d1.y * (s2.x - s1.x)
let m: CGFloat = l / k
let center = CGPoint(x: s2.x + m * d2.x, y: s2.y + m * d2.y)
let dx = center.x - a.x
let dy = center.y - a.y
let radius = sqrt(dx * dx + dy * dy)