Java: Compute the radius and the central coordinate of a circle

Last update on May 13 2025 12:59:00 (UTC/GMT +8 hours)

Compute Circle from Three Points

Write a Java program to compute the radius and central coordinates (x, y) of a circle constructed from three given points on the plane surface.

Input:

x1,y1,x2,y2,x3,y3,xp,yp separated by a single space.

Sample Solution:

Java Code:

// Importing necessary classes for input/output operations
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.BufferedReader;

// Main class named "Main"
class Main {
    // Main method with IOException in case of input error
    public static void main(String[] args) throws IOException {
        // Creating BufferedReader for efficient reading of input
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        // Prompting the user to input coordinates x1, y1, x2, y2, x3, y3 separated by a single space
        System.out.println("Input x1, y1, x2, y2, x3, y3 separated by a single space:");

        // Reading the input line and splitting it into an array of strings
        String[] input = br.readLine().split(" ");

        // Parsing the input strings into double values
        double x1 = Double.parseDouble(input[0]);
        double y1 = Double.parseDouble(input[1]);
        double x2 = Double.parseDouble(input[2]);
        double y2 = Double.parseDouble(input[3]);
        double x3 = Double.parseDouble(input[4]);
        double y3 = Double.parseDouble(input[5]);

        // Calculating intermediate values for further computations
        double A = x2 - x1;
        double B = y2 - y1;
        double p = (y2 * y2 - y1 * y1 + x2 * x2 - x1 * x1) / 2;
        double C = x3 - x1;
        double D = y3 - y1;
        double q = (y3 * y3 - y1 * y1 + x3 * x3 - x1 * x1) / 2;

        // Calculating the coordinates of the center (X, Y) and the radius (r) of the circle
        double X = (D * p - B * q) / (A * D - B * C);
        double Y = (A * q - C * p) / (A * D - B * C);

        double r = Math.sqrt(Math.pow(X - x1, 2.0) + Math.pow(Y - y1, 2.0));

        // Displaying the radius and the central coordinate of the circle
        System.out.println("\nRadius and the central coordinate:");
        System.out.printf("%.3f (%.3f %.3f)", r, X, Y);
    }
}

Sample Output:

Input x1, y1, x2, y2, x3, y3 separated by a single space:
 5 6 4 8 7 9

Radius and the central coordinate:
1.821 (5.786 7.643)

Flowchart:

Flowchart: Java exercises: Compute the radius and the central coordinate of a circle.

For more Practice: Solve these Related Problems:

Write a Java program to compute the circle defined by three points and determine if the points are collinear.
Write a Java program to compute the circle from three points and then calculate its circumference and area.
Write a Java program to compute the circle that passes through three points using a determinant-based method.
Write a Java program to verify the computed circle by checking if a fourth point lies on its circumference.

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Java Code Editor:

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