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

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 circle(center: CGPoint, radius: CGFloat) 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) return Result.circle(center: center, radius: radius) }

**Ask Dr. Math Archives: Finding the Center of a Circle,** Plug the values for the center in any of the three quadratic equations above (I be your 3 points, and let 〈x0,y0〉 represent the center of the circle. let The radius, r, can then be calculated with Pythogoras' theorem, or using matrices again:. Circle radius and centre calculator given 3 points This calculator will work out the radius and centre of a circle which intersects three given points. It sometimes happens that you need 3 points to sit on a circle.

**Equation of a Circle Through Three Points,** This online calculator finds circle passing through three given points. It outputs center and radius of a circle, circle equations and draws a circle on a graph. Center point (x, y) and the radius of a circle passing through 3 points (x 1, y 1) (x 2, y 2) and (x 3, y 3) are: Example 1 - Circle Defined by 3 Points Find the equation of a circle that passes through the points (− 3 , 4) , (4 , 5) and (1 , − 4 ) .

**Example 2 : Equation of a Circle given 3 points on the ,** be defined or drawn any through any three points not in a straight line. So, if you input 3 points, this will compute the circle's center point, radius and equation. Center, Radius and Equation You probably remember from high school geometry that only one circle can be defined or drawn any through any three points not in a straight line. So, if you input 3 points, this will compute the circle's center point, radius and equation. X1= X2= X3=

**Get the equation of a circle when given 3 points,** The perpendicular bisectors of two secant lines intersect at the center. Explanation: Find the slopes of the lines through two pairs of points. This calculator can find the center and radius of a circle given its equation in standard or general form. Also, it can find equation of a circle given its center and radius. The calculator will generate a step by step explanations and circle graph.