# Java Program to Check if a Given Circle Lies Completely Inside the Ring Formed by Two Concentric Circle

In the previous article, we have seen Java Program to Check if a Line Touches or Intersects a Circle

In this article we will discuss about how to check if a given circle lies completely inside the ring formed by two concentric circle using Java programming language.

## Java Program to Check if a Given Circle Lies Completely Inside the Ring Formed by Two Concentric Circle

Before jumping into the program directly, let’s first know how can we Check if a Given Circle Lies Completely Inside the Ring Formed by Two Concentric Circle

Explanation:

r = radius of smaller concentric circle

R = radius of Bigger concentric circle

r1 = radius of the circle to be checked

dist = distance between the origin and center of the circle

Note: The concentric circles are at coordinate(0,0).

If (dist+r1 = R) and (dist-r1 = r) then the circle lies inside the ring.

Example:

When r=4, R=8 and r1=2, Center(6,0)

Distance = sqrt(x*x+y*y)

= sqrt(36+0)

=6

6-2 = 4(r) and 6+2 = 8(R)

Hence it lies inside the ring.

Let’s see different ways to check if a given circle lies completely inside the ring.

### Method-1: Java Program to Check if a Given Circle Lies Completely Inside the Ring Formed by Two Concentric Circle By Using Static Value

Approach:

• Declare the value for all three radiuses and the coordinate of the center.
• Then call the checkCircle() user defined method by passing all the values as parameter.
• In this method the it checks if the distance of the center from the origin and compares it with the radius of the concentric circles.
• Then print the result.

Program:

import java.util.Scanner;
import java.awt.Point;
import static java.lang.Math.*;

public class Main
{
public static void main(String[] args)
{
Scanner scan = new Scanner(System.in);
//Static initialization
int r = 4, R = 8, r1 = 2;
Point circle = new Point(6,0);
// Prints the result
if(circleCheck(r,R,r1,circle))
System.out.println("The circle is inside the ring");
else
System.out.println("The circle is outside the ring");
}

//circleCheck() method
public static boolean circleCheck(int r, int R, int r1, Point circle)
{
// Uses pythagoras theorem to calculate the distance of the circle from origin
int distance = (int)Math.sqrt(circle.x*circle.x + circle.y*circle.y);
// Checks the condition and returns true or false
return (distance - r1 >= r && distance + r1 <= R);
}
}

Output:

The circle is inside the ring

### Method-2: Java Program to Check if a Given Circle Lies Completely Inside the Ring Formed by Two Concentric Circle By User Input Value

Approach:

1. Take user input for all three radiuses and the coordinate of the center.
2. Then call the checkCircle() user defined method by passing all the values as parameter.
3. In this method the it checks if the distance of the center from the origin and compares it with the radius of the concentric circles.
4. Then print the result.

Program:

import java.awt.Point;
import java.util.Scanner;
import static java.lang.Math.*;

public class Main
{
public static void main(String[] args)
{
Scanner scan = new Scanner(System.in);
System.out.println("Enter the radiuses of the small, big and the circle to be checked");
int r = scan.nextInt(), R = scan.nextInt(), r1 = scan.nextInt();
System.out.println("Enter the coordinates of the center of the circle to be checked");
Point circle = new Point(scan.nextInt(),scan.nextInt());
// Prints the result
if(circleCheck(r,R,r1,circle))
System.out.println("The circle is inside the ring");
else
System.out.println("The circle is outside the ring");
}

//circleCheck() method
public static boolean circleCheck(int r, int R, int r1, Point circle)
{
// Uses pythagoras theorem to calculate the distance of the circle from origin
int distance = (int)Math.sqrt(circle.x*circle.x + circle.y*circle.y);
// Checks the condition and returns true or false
return (distance - r1 >= r && distance + r1 <= R);
}
}

Output:

Case-1
Enter the radiuses of the small, big and the circle to be checked
4 8 2
Enter the coordinates of the center of the circle to be checked
5 0
The circle is outside the ring

Case-2
Enter the radiuses of the small, big and the circle to be checked
4 8 2
Enter the coordinates of the center of the circle to be checked
6 0
The circle is inside the ring

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