The following formula gives the distance between two points (x1, y1) and (x2, y2

Question

The following formula gives the distance between two points (x1, y1) and (x2, y2) in the Cartesian plane:

(x2-x1)^2 + (y2-y1)^2

Given the center and a point on a circle, you can use this formula to find the radius of a circle. Write a program that prompts the user to enter the center and a point on the circle. The program should then output the circle’s radius, diameter, circumference, and area. Your program must have at least the following methods:

a. distance: This method takes as its parameters four numbers that represent two points in the plane and returns the distance between them.
b. Radius: This method takes as its parameter four numbers that represent the center and a point on the circle, calls the method distance to find the radius of the circle, and returns the circle’s radius.
c. Circumference: This method takes as its parameter a number that represents the radius of the circle and returns the circle’s circumference. (if r is the radius, the circumference is 2(Pi)r.)
d. Area: This method takes as its parameter a number that represents the radius of the circle and returns the circle’s area. (If r is the radius, the area is (Pi)r^2.)
Assume that Pi =3.1416

Explanation / Answer

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import java.util.*;
public class circle {
    public static final  double pi=3.1416;
    public static void main(String[] args){
       
        Scanner input=new Scanner(System.in);
        double x1,y1,x2,y2;
        double r;
        System.out.println("Enter center of circle ");
        x1=input.nextDouble();
        y1=input.nextDouble();
        System.out.println("Enter point of circle ");
        x2=input.nextDouble();
        y2=input.nextDouble();       
        r=radius(x1,y1,x2,y2);
        System.out.println("Radius of circle "+r);
        System.out.println("Area of circle   "+area(r));
        System.out.println("circumference of circle "+circumference(r));
       
    }
    public static double circumference(double radius){
        return 2*pi*radius;
    }
    public static double area(double radius){
        return pi*radius*radius;
    }
    public static double radius(double x1,double y1,double x2,double y2)
    {
        return distance(x1,y1,x2,y2);
    }
    public static double distance(double x1,double y1,double x2,double y2)
    {
        double p1=Math.pow((x2-x1),2);
        double p2=Math.pow((y2-y1),2);
        return p1+p2;
    }
}

----------------------------------------------------------

Output:

Enter center of circle
2 2
Enter point of circle
3 6
Radius of circle 17.0
Area of circle   907.9223999999999
circumference of circle 106.81439999999999
BUILD SUCCESSFUL (total time: 12 seconds)

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