Check if two given circles touch or intersect each other (original) (raw)

Last Updated : 27 May, 2024

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

Try It Yourself

**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 B 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.

Python

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)

This article is contributed by **Aarti_Rathi and **Dharmendra kumar.