# 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\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

 `= ``\$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
```

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Improved By : vt_m

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