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 and  Y coordinates which denote the center of the new circle to be formed with radius rad, your task is to check whether the circle with coordinates X and 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 =9, 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

Approach: 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 Inner circle, 
• It will fit

Below is the implementation of the above approach:

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)
        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)
        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) :
        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)
            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)
        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)
        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

Time Complexity: O(log n) since using inbuilt sqrt and pow function
Auxiliary Space: O(1)

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