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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



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.



This article is attributed to GeeksforGeeks.org

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