Check if a circle lies inside another circle or not

Given two circles with radii and centres given. The task is to check whether the smaller circle lies inside the bigger circle or not.

Examples:

Input: x1 = 10, y1 = 8, x2 = 1, y2 = 2, r1 = 30, r2 = 10 
Output: The smaller circle lies completely inside
 the bigger circle without touching each other
 at a point of circumference. 


Input :x1 = 7, y1 = 8;x2 = 3, y2 = 5;r1 = 30, r2 = 25
Output :The smaller circle lies completely inside
 the bigger circle with touching each other
 at a point of circumference.

Approach: 
Here three cases can come, 

• The smaller circle lies completely inside the bigger circle without touching each other at a point of circumference. 
  If this case happens, the sum of the distance between the centres and smaller radius is lesser than the bigger radius, then obviously the smaller circle lies completely inside the circle, without touching the circumference.

• The smaller circle lies completely inside the bigger circle with touching each other at a point of the circumference. If this case happens, the sum of the distance between the centres and smaller radius is equal to the bigger radius, then obviously the smaller circle lies completely inside the circle, with touching the circumference.

• The smaller does not lies inside the bigger circle completely.If this case happens, then sum of the distance between the centers and smaller radius is greater than the bigger radius, then obviously the smaller circle does not lies completely inside the circle.

Below is the implementation of the above approach:  

CPP

// C++ program to check if one circle
// lies inside another circle or not.

#include <bits/stdc++.h>
using namespace std;

void circle(int x1, int y1, int x2,
            int y2, int r1, int r2)
{
    int distSq = sqrt(((x1 - x2)
                       * (x1 - x2))
                      + ((y1 - y2)
                         * (y1 - y2)));

    if (distSq + r2 == r1)
        cout << "The smaller circle lies completely"
             << " inside the bigger circle with "
             << "touching each other "
             << "at a point of circumference. "
             << endl;
    else if (distSq + r2 < r1)
        cout << "The smaller circle lies completely"
             << " inside the bigger circle without"
             << " touching each other "
             << "at a point of circumference. "
             << endl;
    else
        cout << "The smaller does not lies inside"
             << " the bigger circle completely."
             << endl;
}

// Driver code
int main()
{
    int x1 = 10, y1 = 8;
    int x2 = 1, y2 = 2;
    int r1 = 30, r2 = 10;
    circle(x1, y1, x2, y2, r1, r2);

    return 0;
}

Java

// Java program to check if one circle
// lies inside another circle or not.
import java.io.*;

class GFG
{

    static void circle(int x1, int y1, int x2,
                int y2, int r1, int r2)
    {
        int distSq = (int)Math.sqrt(((x1 - x2)
                                    * (x1 - x2))
                                    + ((y1 - y2)
                                    * (y1 - y2)));

        if (distSq + r2 == r1)
        {
            System.out.println("The smaller circle lies completely"
                + " inside the bigger circle with "
                + "touching each other "
                + "at a point of circumference. ") ;
        }

        else if (distSq + r2 < r1)
        {
            System.out.println("The smaller circle lies completely"
                + " inside the bigger circle without"
                + " touching each other "
                + "at a point of circumference.") ;
        }

        else
        {
            System.out.println("The smaller does not lies inside"
                + " the bigger circle completely.") ;
        }

    }

    // Driver code
    public static void main (String[] args)
    {
        int x1 = 10, y1 = 8;
        int x2 = 1, y2 = 2;
        int r1 = 30, r2 = 10;
        circle(x1, y1, x2, y2, r1, r2);
    }
}

// This code is contributed by ajit_00023.

Python

# Python3 program to check if one circle
# lies inside another circle or not.

def circle(x1, y1, x2,y2, r1, r2):

    distSq = (((x1 - x2)* (x1 - x2))+ ((y1 - y2)* (y1 - y2)))**(.5)

    if (distSq + r2 == r1):
        print("The smaller circle lies completely"
            " inside the bigger circle with "
            "touching each other "
            "at a point of circumference. ")
    elif (distSq + r2 < r1):
        print("The smaller circle lies completely"
            " inside the bigger circle without"
            " touching each other "
            "at a point of circumference. ")
    else:
        print("The smaller does not lies inside"
            " the bigger circle completely.")

# Driver code
x1 ,y1 = 10,8
x2 ,y2 = 1, 2
r1 ,r2 = 30,10
circle(x1, y1, x2, y2, r1, r2)

# This code is contributed by mohit kumar 29

C#

// C# program to check if one circle
// lies inside another circle or not.
using System;

class GFG
{

    static void circle(int x1, int y1, int x2,
                int y2, int r1, int r2)
    {
        int distSq = (int)Math.Sqrt(((x1 - x2)
                        * (x1 - x2))
                        + ((y1 - y2)
                            * (y1 - y2)));

        if (distSq + r2 == r1)
        {
            Console.WriteLine("The smaller circle lies completely"
                + " inside the bigger circle with "
                + "touching each other "
                + "at a point of circumference. ") ;
        }

        else if (distSq + r2 < r1)
        {
            Console.WriteLine("The smaller circle lies completely"
                + " inside the bigger circle without"
                + " touching each other "
                + "at a point of circumference.") ;
        }

        else
        {
            Console.WriteLine("The smaller does not lies inside"
                + " the bigger circle completely.") ;
        }

    }

    // Driver code
    static public void Main ()
    {
        int x1 = 10, y1 = 8;
        int x2 = 1, y2 = 2;
        int r1 = 30, r2 = 10;
        circle(x1, y1, x2, y2, r1, r2);
    }
}

// This code is contributed by AnkitRai01

Javascript

<script>
// javascript program to check if one circle
// lies inside another circle or not.
function circle(x1 , y1 , x2,
            y2 , r1 , r2)
{
    var distSq = parseInt(Math.sqrt(((x1 - x2)
                                * (x1 - x2))
                                + ((y1 - y2)
                                * (y1 - y2))));

    if (distSq + r2 == r1)
    {
        document.write("The smaller circle lies completely"
            + " inside the bigger circle with "
            + "touching each other "
            + "at a point of circumference. ") ;
    }

    else if (distSq + r2 < r1)
    {
        document.write("The smaller circle lies completely"
            + " inside the bigger circle without"
            + " touching each other "
            + "at a point of circumference.") ;
    }

    else
    {
        document.write("The smaller does not lies inside"
            + " the bigger circle completely.") ;
    }

}

// Driver code
var x1 = 10, y1 = 8;
var x2 = 1, y2 = 2;
var r1 = 30, r2 = 10;
circle(x1, y1, x2, y2, r1, r2);

// This code is contributed by Princi Singh
</script>

Output:
The smaller circle lies completely inside the bigger circle without touching each other at a point of circumference. 

Time Complexity: O(logn) because inbuilt sqrt function is being used

Auxiliary Space: O(1)