# Check if a Point Exists in Circle Sector in Java

A circle is a closed shape formed by tracing a point that moves in a plane such that its distance from a given point is constant. In this article we will check how to form the equation of circle from given radius and centre.

We will be given a circle with point i.e (x, y), radius r and centre i.e (x1, y1). We need to form the equation of circle from given radius and centre. The equation of the circle is given by formula −

$$\mathrm{(x\:-\:x1)^2\:+\:(y\:-\:y1)^2\:=\:r^2}$$

Where,

• (x, y) is a point.

• (x1, y1) is centre.

Now to check if a point exists in a circle sector the point must satisfy the following equation −

$$\mathrm{(x\:-\:x1)^2\:+\:(y\:-\:y1)^2\:<\:r^2}$$

Lets take the centre of the circle as (0, 0).

Let’s see how we can check if a point exists in circle sector by using Java programming language.

## To show you some instances

### Instance-1

• Given inputs for points and radius are −

• Points = (2, 6), Radius = 3

• After checking the condition, the result will be −

• Point does not exist in circle sector.

### Instance-2

• Given inputs for points and radius are −

• Points = (8, 5), Radius = 11

• After checking the condition, the result will be −

• Point exists in circle sector.

### Algorithm

• Step-1 − Declare and initialize the variables.

• Step-2 − Putting the values in formula.

• Step-3 − Check for condition.

• Step-4 − Print the result.

## Multiple Approaches

We have provided the solution in different approaches.

• By Using Static Inputs

• By Using User Defined Method

Let’s see the program along with its output one by one.

## Approach-1: By Using Static Input

In this approach, value of point and radius will be initialized in the program. Then as per the algorithm we will find if a point exists in circle sector.

### Example

public class Main{
//main method
public static void main(String arr[]){

//declaring variables
double x = 2, y = 6, r = 3;

//applying logic
double m = x * x;
double n = y * y;
double o = r * r;
double p = m + n;

//checking the condition
if (p < o) {

//print if point lie inside circle
System.out.println("Point exist in circle sector.");
} else {

//print if point does not lie inside circle
System.out.println("Point does not exist in circle sector.");
}
}
}


### Output

Point does not exist in circle sector.


## Approach-2: By Using User Defined Method

In this approach, value of point and radius will be initialized in the program. Then call a user defined method by passing the given values and inside method as per the algorithm we will find if a point exists in circle sector.

### Example

public class Main{
//main method
public static void main(String arr[]){

//declaring variables
double x = 8, y = 5, r = 11;

//calling user defined method
sector_circle(x, y, r);
}

//user defined method
static void sector_circle(double x, double y, double r){

//applying logic
double m = x * x;
double n = y * y;
double o = r * r;
double p = m + n;

//checking the condition
if (p < o) {

//print if point lie inside circle
System.out.println("Point exists in circle sector.");
} else {

//print if point does not lie inside circle
System.out.println("Point does not exist in circle sector.");
}
}
}


### Output

Point exists in circle sector.


In this article, we explored different approaches to check if a point exists in a circle sector by using Java programming language.

Updated on: 04-May-2023

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