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 <bits/stdc++.h>
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 code
int 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 other
def 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, 8
x2, y2 = 14, -24
r1, r2 = 30, 10

# Function call
circle(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 code
var 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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