# 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 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; }

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## 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

 = \$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

## tags:

Geometric circle Geometric