# Java Program to Find Angle of Intersection of Two Circles Having Their Centers D Distance Apart

In the previous article, we have discussed about Java Program to Find Interior and Exterior Angle of Regular Polygon when Number of Sides of Polygon is Given

In this article we are going to see how to find angle of intersection of two circles having their centers D distance apart by using Java programming language.

## Java Program to Find Angle of Intersection of Two Circles Having Their Centers D Distance Apart

Suppose there are two circles say Circle1 and Circle2 intersecting each-other.

Both circles are having radius R1 and R2 respectively.

Having distance D from the center A and B

Now, we need to find the angle of intersection of the 2 circles.

In triangle AOB by using Pythagoras theorem

AOB = (R12 + R22 – D2) / (2 * R1 * R2)

Example:

R1 = 3
R2 = 4
D = 5

Cos a =  (R1*R1 +R2*R2-D*D)/(2*R1*R2) = 25/24 = 0

Let’s see different ways to find angle of intersection of two circles having their centers D distance apart.

### Method-1: Java Program to Find Angle of Intersection of Two Circles Having Their Centers D Distance Apart By Using Static Input Value

Approach:

• Declare an double variable say ‘R1’ and assign the value to it, which holds the radius of the circle Circle1.
• Declare an double variable say ‘R2’ and assign the value to it, which holds the radius of the circle Circle2.
• Declare an double variable say ‘D’ and assign the value to it, which holds the distance between the centers of 2 circles.
• Find the intersection angle using the formula Cos a = (R12 +R22-D2)/(2*R1*R2)
• Print the result

Program:

import java.io.*;
class Main
{
public static void main(String [] args)
{
double R1 = 3;
double R2 =  4;
double D =  5;
// formula to find angle of intersection
double a = (R1*R1 +R2*R2-D*D)/(2*R1*R2);
System.out.println("The angle of intersection of 2 circle is " + a + " rad");
}
}

Output:

The angle of intersection of 2 circle is 0.0 rad

### Method-2: Java Program to Find Angle of Intersection of Two Circles Having Their Centers D Distance Apart By Using User Input Value

Approach:

• Declare an double variable say ‘R1’ which holds the radius of the circle Circle1.
• Declare an double variable say ‘R2’ which holds the radius of the circle Circle2.
• Declare an double variable say ‘D’ which holds the distance between the centers of 2 circles.
• Then we will take the value of “R1”, “R2”, “D” as user input using scanner class.
• Find the intersection angle using the formula Cos a = (R12 +R22-D2)/(2*R1*R2)
• Print the result.

Program:

import java.io.*;
import java.util.Scanner;
class Main
{
public static void main(String [] args)
{
// scanner class obj ref
Scanner s = new Scanner(System.in);
System.out.println("Enter the radius of the circle C1");
// to take user input value
double R1 = s.nextDouble();
System.out.println("Enter the radius of the circle C2");
double R2 = s.nextDouble();
System.out.println("Enter the distance between 2 centers");
double D = s.nextDouble();
// formula to find angle of intersection
double a = (R1*R1 +R2*R2-D*D)/(2*R1*R2);
System.out.println("The angle of intersection of 2 circle is " + a + " rad");
}
}


Output:

Enter the radius of the circle C1
8
Enter the radius of the circle C2
6
Enter the distance between 2 centers
10
The angle of intersection of 2 circle is 0.0 rad

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