# 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```

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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 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.``?>`

## Javascript

 ``

Output:

`Doesn't Fit`

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