# 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 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

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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 <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.` `?>` |

## Javascript

`<script>` ` ` `// Javascript 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` ` ` `var` `val = Math.sqrt(Math.pow(x, 2) + Math.pow(y, 2));` ` ` ` ` `// Checking the corners of circle` ` ` `if` `(val + rad <= R && val - rad >= R - r) ` ` ` `document.write( ` `"Fits<br>"` `); ` ` ` `else` ` ` `document.write( ` `"Doesn't Fit<br>"` `);` `}` ` ` `// driver program` `// Radius of outer circle and inner circle` `// respectively` `var` `R = 8, r = 4;` ` ` `// Co-ordinates and radius of the circle` `// to be checked ` `var` `x = 5, y = 3, rad = 3;` `fitOrNotFit(R, r, x, y, rad);` ` ` ` ` `</script>` |

Output:

Doesn't Fit

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