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# Check if two given circles touch or intersect each other

There are two circles A and B with their centres C1(x1, y1) and C2(x2, y2) and radius R1 and R2. The task is to check both circles A and B touch each other or not.

Examples :

Input : C1 = (3,  4)
C2 = (14, 18)
R1 = 5, R2 = 8
Output : Circles do not touch each other.

Input : C1 = (2,  3)
C2 = (15, 28)
R1 = 12, R2 = 10
Output : Circles intersect with each other.

Input : C1 = (-10,  8)
C2 = (14, -24)
R1 = 30, R2 = 10

Approach:
Distance between centres C1 and C2 is calculated as

C1C2 = sqrt((x1 – x2)2 + (y1 – y2)2).

There are three conditions that arise.

1. If C1C2 <= R1 – R2: Circle B is inside A.
2. If C1C2 <= R2 – R1: Circle A is inside B.
3. If C1C2 < R1 + R2: Circle intersects each other.
4. If C1C2 == R1 + R2: Circle A and B are in touch with each other.
5. Otherwise, Circle A and  do not overlap

Below is the implementation of the above approach:

## C++

 // C++ program to check if two// circles touch each other or not.#include using namespace std; int circle(int x1, int y1, int x2, int y2, int r1, int r2){    double d = sqrt((x1 - x2) * (x1 - x2)                         + (y1 - y2) * (y1 - y2));     if (d <= r1 - r2) {        cout << "Circle B is inside A";    }    else if (d <= r2 - r1) {        cout << "Circle A is inside B";    }    else if (d < r1 + r2) {        cout << "Circle intersect to each other";    }    else if (d == r1 + r2) {        cout << "Circle touch to each other";    }    else {        cout << "Circle not touch to each other";    }} // Driver codeint main(){    int x1 = -10, y1 = 8;    int x2 = 14, y2 = -24;    int r1 = 30, r2 = 10;    circle(x1, y1, x2, y2, r1, r2);     return 0;}

## Java

 // Java program to check if two// circles touch each other or not.import java.io.*; class GFG {    static void circle(int x1, int y1, int x2, int y2,                       int r1, int r2)    {        double d = Math.sqrt((x1 - x2) * (x1 - x2)                             + (y1 - y2) * (y1 - y2));         if (d <= r1 - r2) {            System.out.println("Circle B is inside A");        }        else if (d <= r2 - r1) {            System.out.println("Circle A is inside B");        }        else if (d < r1 + r2) {            System.out.println("Circle intersect"                               + " to each other");        }        else if (d == r1 + r2) {            System.out.println("Circle touch to"                               + " each other");        }        else {            System.out.println("Circle not touch"                               + " to each other");        }    }     // Driver code    public static void main(String[] args)    {        int x1 = -10, y1 = 8;        int x2 = 14, y2 = -24;        int r1 = 30, r2 = 10;        circle(x1, y1, x2, y2, r1, r2);    }} // This article is contributed by vt_m.

## Python3

 # Python program to check if two# circles touch each other or not. import math # Function to check if two circles touch each otherdef circle(x1, y1, x2, y2, r1, r2):    d = math.sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2))     if(d <= r1 - r2):        print("Circle B is inside A")    elif(d <= r2 - r1):        print("Circle A is inside B")    elif(d < r1 + r2):        print("Circle intersect to each other")    elif(d == r1 + r2):        print("Circle touch to each other")    else:        print("Circle not touch to each other") # Driver code x1, y1 = -10, 8x2, y2 = 14, -24r1, r2 = 30, 10 # Function callcircle(x1, y1, x2, y2, r1, r2) # This code is contributed by Aman Kumar

## C#

 // C# program to check if two// circles touch each other or not.using System; class GFG {    static void circle(int x1, int y1, int x2, int y2,                    int r1, int r2)    {        double d = Math.Sqrt((x1 - x2) * (x1 - x2)                            + (y1 - y2) * (y1 - y2));         if (d <= r1 - r2) {            Console.Write("Circle B is inside A");        }        else if (d <= r2 - r1) {            Console.Write("Circle A is inside B");        }        else if (d < r1 + r2) {            Console.Write("Circle intersect"                            + " to each other");        }        else if (d == r1 + r2) {            Console.Write("Circle touch to"                            + " each other");        }        else {            Console.Write("Circle not touch"                            + " to each other");        }    }     // Driver code    public static void Main(String[] args)    {        int x1 = -10, y1 = 8;        int x2 = 14, y2 = -24;        int r1 = 30, r2 = 10;        circle(x1, y1, x2, y2, r1, r2);    }} // This article is contributed by Pushpesh Raj.

## Javascript

 // JavaScript program to check if two circles touch each other or not. function circle(x1, y1, x2, y2, r1, r2) {    var d = Math.sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));     if (d <= r1 - r2) {        console.log("Circle B is inside A");    } else if (d <= r2 - r1) {        console.log("Circle A is inside B");    } else if (d < r1 + r2) {        console.log("Circle intersect to each other");    } else if (d === r1 + r2) {        console.log("Circle touch to each other");    } else {        console.log("Circle not touch to each other");    }} // Driver codevar x1 = -10, y1 = 8;var x2 = 14, y2 = -24;var r1 = 30, r2 = 10;circle(x1, y1, x2, y2, r1, r2);// this code is contributed by devendra

Output

Circle touch to each other

Time Complexity: O(log(n)) because using inbuilt sqrt function
Auxiliary Space: O(1)

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