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Check if two given circles touch or intersect each other
  • Difficulty Level : Easy
  • Last Updated : 29 Apr, 2021

There are two circle A and B with their centers C1(x1, y1) and C2(x2, y2) and radius R1 and R2. 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
Input : -10 8
        14 -24 
        30 10
Output : Circle touch each other.

 

 

Distance between centers C1 and C2 is calculated as
 C1C2 = sqrt((x1 - x2)2 + (y1 - y2)2).
There are three condition arises.
1. If C1C2 == R1 + R2
     Circle A and B are touch to each other.
2. If C1C2 > R1 + R2
     Circle A and B are not touch to each other.
3. If C1C2 < R1 + R2
      Circle intersects each other.

 

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)
{
    int distSq = (x1 - x2) * (x1 - x2) +
                 (y1 - y2) * (y1 - y2);
    int radSumSq = (r1 + r2) * (r1 + r2);
    if (distSq == radSumSq)
        return 1;
    else if (distSq > radSumSq)
        return -1;
    else
        return 0;
}
 
// Driver code
int main()
{
    int x1 = -10, y1 = 8;
    int x2 = 14, y2 = -24;
    int r1 = 30, r2 = 10;
    int t = circle(x1, y1, x2,
                   y2, r1, r2);
    if (t == 1)
        cout << "Circle touch to"
             << " each other.";
    else if (t < 0)
        cout << "Circle not touch"
             << " to each other.";
    else
        cout << "Circle intersect"
             << " to each other.";
    return 0;
}

Java




// Java program to check if two
// circles touch each other or not.
import java.io.*;
 
class GFG
{
    static int circle(int x1, int y1, int x2,
                      int y2, int r1, int r2)
    {
        int distSq = (x1 - x2) * (x1 - x2) +
                     (y1 - y2) * (y1 - y2);
        int radSumSq = (r1 + r2) * (r1 + r2);
        if (distSq == radSumSq)
            return 1;
        else if (distSq > radSumSq)
            return -1;
        else
            return 0;
    }
 
    // Driver code
    public static void main (String[] args)
    {
        int x1 = -10, y1 = 8;
        int x2 = 14, y2 = -24;
        int r1 = 30, r2 = 10;
        int t = circle(x1, y1, x2,
                       y2, r1, r2);
        if (t == 1)
            System.out.println ( "Circle touch to" +
                                 " each other.");
        else if (t < 0)
            System.out.println ( "Circle not touch" +
                                 " to each other.");
        else
            System.out.println ( "Circle intersect" +
                                 " to each other.");
             
    }
}
 
// This article is contributed by vt_m.

Python3




# Python3 program to
# check if two circles touch
# each other or not.
 
def circle(x1, y1, x2, y2, r1, r2):
  
    distSq = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
    radSumSq = (r1 + r2) * (r1 + r2);
    if (distSq == radSumSq):
        return 1
    elif (distSq > radSumSq):
        return -1
    else:
        return 0
  
 
# Driver code
x1 = -10
y1 = 8
x2 = 14
y2 = -24
r1 = 30
r2 = 10
 
t = circle(x1, y1, x2, y2, r1, r2)
if (t == 1):
    print("Circle touch to each other.")
elif (t < 0):
    print("Circle not touch to each other.")
else:
    print("Circle intersect to each other.")
 
# This code is contributed by
# Smitha Dinesh Semwal

C#




// C# program to check if two
// circles touch each other or not.
using System;
 
class GFG
{
    static int circle(int x1, int y1, int x2,
                      int y2, int r1, int r2)
    {
        int distSq = (x1 - x2) * (x1 - x2) +
                     (y1 - y2) * (y1 - y2);
        int radSumSq = (r1 + r2) * (r1 + r2);
        if (distSq == radSumSq)
            return 1;
        else if (distSq > radSumSq)
            return -1;
        else
            return 0;
    }
 
    // Driver code
    public static void Main ()
    {
        int x1 = -10, y1 = 8;
        int x2 = 14, y2 = -24;
        int r1 = 30, r2 = 10;
        int t = circle(x1, y1, x2,
                       y2, r1, r2);
        if (t == 1)
            Console.WriteLine ( "Circle touch" +
                             " to each other.");
        else if (t < 0)
            Console.WriteLine( "Circle not touch" +
                                " to each other.");
        else
            Console.WriteLine ( "Circle intersect" +
                                 " to each other.");
             
    }
}
 
// This code is contributed by vt_m.

PHP




<?php
// PHP program to check if two
// circles touch each other or not.
 
function circle($x1, $y1, $x2,
                $y2, $r1, $r2)
{
    $distSq = ($x1 - $x2) * ($x1 - $x2) +
              ($y1 - $y2) * ($y1 - $y2);
    $radSumSq = ($r1 + $r2) * ($r1 + $r2);
    if ($distSq == $radSumSq)
        return 1;
    else if ($distSq > $radSumSq)
        return -1;
    else
        return 0;
}
 
// Driver code
$x1 = -10; $y1 = 8;
$x2 = 14; $y2 = -24;
$r1 = 30; $r2 = 10;
$t = circle($x1, $y1, $x2,
            $y2, $r1, $r2);
if ($t == 1)
    echo "Circle touch to each other.";
else if ($t < 0)
    echo "Circle not touch to each other.";
else
    echo "Circle intersect to each other.";
 
// This code is contributed by vt_m.
?>

Javascript




<script>
 
// JavaScript program to check if two
// circles touch each other or not.
 
function circle(x1, y1, x2,
                      y2, r1, r2)
    {
        let distSq = (x1 - x2) * (x1 - x2) +
                     (y1 - y2) * (y1 - y2);
        let radSumSq = (r1 + r2) * (r1 + r2);
        if (distSq == radSumSq)
            return 1;
        else if (distSq > radSumSq)
            return -1;
        else
            return 0;
    }
 
// Driver Code
        let x1 = -10, y1 = 8;
        let x2 = 14, y2 = -24;
        let r1 = 30, r2 = 10;
        let t = circle(x1, y1, x2,
                       y2, r1, r2);
        if (t == 1)
            document.write ( "Circle touch to" +
                                 " each other.");
        else if (t < 0)
            document.write( "Circle not touch" +
                                 " to each other.");
        else
            document.write ( "Circle letersect" +
                                 " to each other.");
  
 // This code is contributed by susmitakundugoaldanga.
</script>

Output : 
 

Circle touch to each other.

This article is contributed by Dharmendra kumar. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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