Check whether given circle resides in boundary maintained by two other circles

Given outer circle radius R and inner circle radius r, making circles from same center and forming boundary between them. Now, given X,Y co-ordinates which denotes center of new circle to be formed with radius rad, your task is to check whether the circle with co-ordinate X,Y as center can fit in the boundary of circles formed or not.

Examples:

Input : R = 8, r = 4
x = 5, y = 3, rad = 1
Output : Fits

Input :  R = 8, r = 4
x = 5, y = 3,  rad = 3.
Output : Doesn't Fit

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

1 – Doesn’t fits
2 – Fits

The idea is to calculate the distance between the center (0, 0) and the co-ordinates of the circle to be checked. If distance + radius (of the circle to be checked) is less than or equal to Outer Radius and distance – radius (of the circle to be checked) is greater than or equal to Radius of Outer circle – Radius Inner circle
It fits.

Here is the implementation :

C++

// CPP program to check whether circle with given  
// co-ordinates reside within the boundary  
// of outer circle and inner circle 
#include <bits/stdc++.h> 
using namespace std; 
  
// function to check if given circle fit in  
// boundary or not  
void fitOrNotFit(int R, int r, int x, int y, 
                                 int rad) { 
          
    // Distance from the center 
    double val = sqrt(pow(x, 2) + pow(y, 2)); 
      
    // Checking the corners of circle 
    if (val + rad <= R && val - rad >= R - r)     
        cout << "Fits
";     
    else
        cout << "Doesn't Fit
"; 
} 
  
// driver program 
int main() 
{ 
    // Radius of outer circle and inner circle 
    // respectively 
    int R = 8, r = 4; 
      
    // Co-ordinates and radius of the circle 
    // to be checked  
    int x = 5, y = 3, rad = 3; 
    fitOrNotFit(R, r, x, y, rad); 
    return 0; 
} 

/div>

Java

// Java program to check whether circle with given  
// co-ordinates reside within the boundary  
// of outer circle and inner circle 
import java.util.*; 
  
class GFG 
{ 
// function to check if given circle fit in  
// boundary or not  
static void fitOrNotFit(int R, int r, int x, int y, 
                                        int rad) 
{ 
    // Distance from the center 
    double val = Math.sqrt(Math.pow(x, 2) +  
                           Math.pow(y, 2)); 
      
    // Checking the corners of circle 
    if (val + rad <= R && val - rad >= R - r)  
        System.out.println("Fits");  
    else
    System.out.println("Doesn't Fit");      
} 
  
// driver program 
public static void main (String[] args) 
{ 
    // Radius of outer circle and inner circle 
    // respectively 
    int R = 8, r = 4; 
      
    // Co-ordinates and radius of the circle 
    // to be checked  
    int x = 5, y = 3, rad = 3; 
    fitOrNotFit(R, r, x, y, rad); 
} 
} 
/* This Code is contributed by Kriti Shukla */

Python3

# Python3 program to check 
# whether circle with given  
# co-ordinates reside 
# within the boundary  
# of outer circle 
# and inner circle 
  
import math 
  
# function to check if 
# given circle fit in  
# boundary or not  
def fitOrNotFit(R, r, x, y, rad) : 
          
    # Distance from the center 
    val = math.sqrt(math.pow(x, 2) + math.pow(y, 2))  
      
    # Checking the corners of circle 
    if (val + rad <= R and val - rad >= R - r) : 
        print("Fits
")   
    else: 
        print("Doesn't Fit")  
   
  
# driver program 
   
# Radius of outer circle and inner circle 
# respectively 
R = 8
r = 4 
      
# Co-ordinates and radius of the circle 
# to be checked  
x = 5
y = 3
rad = 3 
  
fitOrNotFit(R, r, x, y, rad)  
  
# This code is contributed by  
# Smitha Dinesh Semwal 

C#

// C# program to check whether circle with given  
// co-ordinates reside within the boundary  
// of outer circle and inner circle 
using System; 
  
class GFG 
{ 
    // function to check if given circle fit in  
    // boundary or not  
    static void fitOrNotFit(int R, int r, int x, int y, 
                                            int rad) 
    { 
        // Distance from the center 
        double val = Math.Sqrt(Math.Pow(x, 2) +  
                               Math.Pow(y, 2)); 
           
        // Checking the corners of circle 
        if (val + rad <= R && val - rad >= R - r)  
            Console.WriteLine("Fits");  
        else
        Console.WriteLine("Doesn't Fit");      
    } 
       
    // Driver program 
    public static void Main () 
    { 
        // Radius of outer circle and inner circle 
        // respectively 
        int R = 8, r = 4; 
           
        // Co-ordinates and radius of the circle 
        // to be checked  
        int x = 5, y = 3, rad = 3; 
        fitOrNotFit(R, r, x, y, rad); 
    } 
} 
  
// This Code is contributed by Anant Agarwal. 

PHP

<?php 
// PHP program to check whether 
// circle with given co-ordinates  
// reside within the boundary  
// of outer circle and inner circle 
  
// function to check if given   
// circle fit in boundary or not  
function fitOrNotFit($R, $r, $x, $y, 
                               $rad)  
{ 
          
    // Distance from the center 
    $val = sqrt(pow($x, 2) + pow($y, 2)); 
      
    // Checking the corners of circle 
    if ($val + $rad <= $R && $val -  
                  $rad >= $R - $r)  
        echo"Fits
";  
    else
        echo "Doesn't Fit
"; 
} 
  
    // Driver Code 
  
    // Radius of outer circle and  
    // inner circle respectively 
    $R = 8; $r = 4; 
      
    // Co-ordinates and radius of  
    // the circle to be checked  
    $x = 5; $y = 3; $rad = 3; 
    fitOrNotFit($R, $r, $x, $y, $rad); 
      
// This Code is contributed by vt_m. 
?> 

Output:

Doesn't Fit

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

Check whether given circle resides in boundary maintained by two other circles

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

PHP

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