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

• Difficulty Level : Hard
• Last Updated : 07 Nov, 2021

Given outer circle radius R and inner circle radius r, making circles from the same center and forming the boundary between them. Now, given X, Y coordinates which denotes the center of the new circle to be formed with radius rad, your task is to check whether the circle with coordinate X, Y as the 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 fit
2 – Fits
The idea is to calculate the distance between the center (0, 0) and the coordinates 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 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 programint 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 circleimport 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 programpublic 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# respectivelyR = 8r = 4       # Co-ordinates and radius of the circle# to be checked x = 5y = 3rad = 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 circleusing 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

 = \$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.?>

Javascript



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 write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.