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: FitsInput: R =9, r = 4, x = 5, y = 3, rad = 1
Output: FitsInput : 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 programint 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 circleimport 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 programpublic 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 circleimport 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# respectivelyR = 8r = 4 # Co-ordinates and radius of the circle# to be checked x = 5y = 3rad = 3fitOrNotFit(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 circleusing 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// respectivelyvar 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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