How to check if two given circles are tangent or intersect in Java?

A circle is a closed shape formed by tracing a point moving on a plane such that it is a constant distance from a given point. In this article, we will check whether two given circles touch or intersect each other.

We will get two circles with center 1, i.e. (x1, y1), center 2, i.e. (x2,y2), and radii R1 and R2. We need to check if the given circle collides with another circle, so there are five possible cases -

• Circle 2 is inside circle 1

• Circle 1 is inside circle 2

• Circle 1 and Circle 2 intersect

• Circle 1 and Circle 2 are touching each other

• Circle 1 and Circle 2 do not overlap

Now to check the above condition, we will find the distance between center 1 and center 2 and name it "d".

Now,

• 1. If d

• 2. If d

• 3. If d

• 4. If d == R1 R2: Circle 1 and Circle 2 touch each other

• 5. Otherwise, Circle 1 and Circle 2 do not overlap

"d" can be found using the formula -

$$\mathrm{d\:=\:sqrt((x1\:–\:x2)^2\: \:(y1\:–\:y2)^2}$$

let's start!

Show you some examples

Example 1

• The given input for "d" is -

• Center 1 = (9, 3), Center 2 = (11, 1), R1 = 5, R2 = 4.

• After finding the value of "d", the result will be -

• Circle 1 and Circle 2 intersect

Example 2

• The given input for "d" is -

• Center 1 = (5, 8), Center 2 = (9, 11), R1 = 20, R2 = 40.

• After finding the value of "d", the result will be -

• Circle 1 is inside circle 2

algorithm

• Step-1 - Declare and initialize variables.

• Step-2 - Find the distance between center 1 and center 2 of the circle.

• Step-3 - Check the five conditions for distance.

• Step 4 - Print the results.

Multiple methods

We provide solutions in different ways.

• By using static input

• By using user-defined methods

Let’s look at the program and its output one by one.

Method 1: Use static input

In this method, the values ​​of radius 1 and radius 2, center 1 and center 2 will be assigned to find "d". Then based on the algorithm we find out whether the line touches, intersects or lies outside the circle.

Example

public class Main {
   //main method
   public static void main(String[] args){
      
      //declaring variables
      int x1 = 9, y1 = 3;
      int x2 = 11, y2 = 1;
      int r1 = 5, r2 = 4;
	      
      //finding d using the formula
      double d = Math.sqrt((x1 - x2) * (x1 - x2)	+ (y1 - y2) * (y1 - y2));
      if (d <= r1 - r2) {
		   //print if Circle 2 lie inside circle 1
         System.out.println("Circle 2 lie inside circle 1");
      }
      else if (d <= r2 - r1) {
         
         //print if Circle 1 lie inside 2
         System.out.println("Circle 1 lie inside 2");
      }
      else if (d < r1 + r2) {
         
         //print if Circle 1 and 2 intersect each other
         System.out.println("Circle 1 and 2 intersect each other");
      }
      else if (d == r1 + r2) {
		   
         //print if Circle 1 and 2 touch each other
         System.out.println("Circle 1 and 2 touch each other");
      } else {
		   
         //print if Circle 1 and 2 do not touch each other
         System.out.println("Circle 1 and 2 do not touch each other");
      }
   }
} 

Output

Circle 1 and 2 intersect each other

Method 2: Using user-defined methods

In this method, the values ​​of radius 1 and radius 2, center 1 and center 2 will be assigned to find "d". Then the user defined method is called by passing the given value and according to the algorithm we will find if the straight lines touch, intersect or lie outside the circle.

Example

public class Main {
   //main method
   public static void main(String[] args){
	   
      //declaring variables
      int x1 = 5, y1 = 8;
      int x2 = 9, y2 = 11;
      int r1 = 20, r2 = 40;
		
      //calling user defined method
      func(x1, y1, x2, y2, r1, r2);
   }
   
   //user defined method
   static void func(int x1, int y1, int x2, int y2, int r1, int r2){
	   
      //finding d using the formula
      double d = Math.sqrt((x1 - x2) * (x1 - x2)	+ (y1 - y2) * (y1 - y2));
      if (d <= r1 - r2) {
		   
         //print if Circle 2 lie inside circle 1
         System.out.println("Circle 2 lie inside circle 1");
      }
      else if (d <= r2 - r1) {
		   
         //print if Circle 1 lie inside 2
         System.out.println("Circle 1 lie inside 2");
      }
      else if (d < r1 + r2) {
		   
         //print if Circle 1 and 2 intersect each other
         System.out.println("Circle 1 and 2 intersect each other");
      }
      else if (d == r1 + r2) {
		   
         //print if Circle 1 and 2 touch each other
         System.out.println("Circle 1 and 2 touch each other");
      }
      else {
		   
         //print if Circle 1 and 2 do not touch each other
         System.out.println("Circle 1 and 2 do not touch each other");
      }
   }
} 

Output

Circle 1 lie inside 2

In this article, we explored different ways to find whether two given circles touch or intersect each other using the Java programming language.

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