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:**

- Take user input 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.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); //Asking the user for input 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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