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Check whether given circle resides in boundary maintained by two other circles
  • Difficulty Level : Hard
  • Last Updated : 06 May, 2018

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\n";    
    else
        cout << "Doesn't Fit\n";
}
  
// 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;
}

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\n")  
    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\n"
    else
        echo "Doesn't Fit\n";
}
  
    // 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

This article is contributed by Rohit Thapliyal. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.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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