Skip to content
Related Articles

Related Articles

Check whether a point exists in circle sector or not.
  • Difficulty Level : Medium
  • Last Updated : 31 Mar, 2021

We have a circle centered at origin (0, 0). As input we are given with starting angle of the circle sector and the size of the circle sector in percentage. 

Examples: 

Input :  Radius = 8 
         StartAngle = 0 
         Percentage = 12 
         x = 3 y = 4 
Output : Point (3, 4) exists in the circle 
         sector

Input : Radius = 12 
        Startangle = 45
        Percentage = 25  
        x = 3 y = 4 
Output : Point (3, 4) does not exist in 
         the circle sector

 

Source:wikibooks.org

Source:wikibooks.org

In this image starting angle is 0 degree, radius r and suppose that percentage of colored area is 12% then we calculate Ending Angle as 360/percentage + starting angle.

To find whether a point (x, y) exists in a circle sector (centered at origin) or not we find polar coordinates of that point and then go through the following steps:



  1. Convert x, y to polar coordinates using this 
    Angle = atan(y/x); Radius = sqrt(x * x + y * y);
  2. Then Angle must be between StartingAngle and EndingAngle, and Radius between 0 and your Radius.

C++




// C++ program to check if a point lies inside a circle
// sector.
#include<bits/stdc++.h>
using namespace std;
 
void checkPoint(int radius, int x, int y, float percent,
                                         float startAngle)
{
    // calculate endAngle
    float endAngle = 360/percent + startAngle;
 
    // Calculate polar co-ordinates
    float polarradius = sqrt(x*x+y*y);
    float Angle = atan(y/x);
 
    // Check whether polarradius is less then radius of circle
    // or not and Angle is between startAngle and endAngle
    // or not
    if (Angle>=startAngle && Angle<=endAngle && polarradius<radius)
        printf("Point (%d, %d) exist in the circle sector\n", x, y);
    else
        printf("Point (%d, %d) does not exist in the circle sector\n",
                                                              x, y);
}
 
// Driver code
int main()
{
    int radius = 8, x = 3, y = 4;
    float percent  = 12, startAngle = 0;
    checkPoint(radius, x, y, percent, startAngle);
    return 0;
}

Java




// Java program to check if
// a point lies inside a circle
// sector.
 
class GFG
{
static void checkPoint(int radius, int x, int y, float percent,
                                         float startAngle)
{
 
    // calculate endAngle
    float endAngle = 360/percent + startAngle;
  
    // Calculate polar co-ordinates
    double polarradius = Math.sqrt(x*x+y*y);
    double Angle = Math.atan(y/x);
  
    // Check whether polarradius is
    // less then radius of circle
    // or not and Angle is between
    // startAngle and endAngle
    // or not
    if (Angle>=startAngle && Angle<=endAngle && polarradius<radius)
        System.out.print("Point"+"("+x+","+y+")"+
        " exist in the circle sector\n");
    else
        System.out.print("Point"+"("+x+","+y+")"+
        " exist in the circle sector\n");
}
 
// Driver Program to test above function
public static void main(String arg[])
{
    int radius = 8, x = 3, y = 4;
    float percent  = 12, startAngle = 0;
    checkPoint(radius, x, y, percent, startAngle);
}
}
 
// This code is contributed
// by Anant Agarwal.

Python3




# Python3 program to check if a point
# lies inside a circle sector.
import math
 
def checkPoint(radius, x, y, percent, startAngle):
 
    # calculate endAngle
    endAngle = 360 / percent + startAngle
 
    # Calculate polar co-ordinates
    polarradius = math.sqrt(x * x + y * y)
    Angle = math.atan(y / x)
 
    # Check whether polarradius is less
    # then radius of circle or not and
    # Angle is between startAngle and
    # endAngle or not
    if (Angle >= startAngle and Angle <= endAngle
                        and polarradius < radius):
        print("Point (", x, ",", y, ") "
              "exist in the circle sector")
    else:
        print("Point (", x, ",", y, ") "
              "does not exist in the circle sector")
 
# Driver code
radius, x, y = 8, 3, 4
percent, startAngle = 12, 0
 
checkPoint(radius, x, y, percent, startAngle)
 
# This code is contributed by
# Smitha Dinesh Semwal

C#




// C# program to check if a point lies
// inside a circle sector.
using System.IO;
using System;
 
class GFG {
     
    static void checkPoint(int radius, int x, int y,
                    float percent, float startAngle)
    {
         
        // calculate endAngle
        float endAngle = 360 / percent + startAngle;
     
        // Calculate polar co-ordinates
        float polarradius =
                    (float)Math.Sqrt(x * x + y * y);
                     
        float Angle = (float)Math.Atan(y / x);
     
        // Check whether polarradius is less then
        // radius of circle or not and Angle is
        // between startAngle and endAngle or not
        if (Angle >= startAngle && Angle <= endAngle
                            && polarradius < radius)
            Console.Write("Point ({0}, {1}) exist in "
                         + "the circle sector", x, y);
        else
            Console.Write("Point ({0}, {1}) does not "
                + "exist in the circle sector", x, y);
    }
     
    // Driver code
    public static void Main()
    {
        int radius = 8, x = 3, y = 4;
        float percent = 12, startAngle = 0;
        checkPoint(radius, x, y, percent, startAngle);
    }
}
 
// This code is contributed by Smitha Dinesh Semwal

Javascript




<script>
 
// Javascript program to check if
// a point lies inside a circle
// sector.
function checkPoint(radius, x, y, percent, startAngle)
{
     
    // Calculate endAngle
    let endAngle = 360 / percent + startAngle;
    
    // Calculate polar co-ordinates
    let polarradius = Math.sqrt(x * x + y * y);
    let Angle = Math.atan(y / x);
    
    // Check whether polarradius is
    // less then radius of circle
    // or not and Angle is between
    // startAngle and endAngle
    // or not
    if (Angle >= startAngle &&
        Angle <= endAngle &&
        polarradius < radius)
        document.write("Point" + "(" + x + 
                       "," + y + ")" +
        " exist in the circle sector\n");
    else
        document.write("Point" + "(" + x +
                       "," + y + ")" +
        " exist in the circle sector\n");
}
      
// Driver code   
let radius = 8, x = 3, y = 4;
let percent  = 12, startAngle = 0;
 
checkPoint(radius, x, y, percent, startAngle);
 
// This code is contributed by splevel62
           
</script>

Output : 

Point(3, 4) exists in the circle sector

Time complexity = O(1)

This article is contributed by Niteesh kumar. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 

My Personal Notes arrow_drop_up