Distance between two centers of circles - Java Program to Find Distance between Centers of Two Intersecting Circles if the Radius and Common Chord Length is Given

Distance between two centers of circles: In the previous article, we have discussed about Java Program to Find Ratio of the distance between the Centers of the Circles and the Point of Intersection of Two Direct Common Tangents to the Circles

In this article we are going to see how to find distance between centers of two intersecting circles if the radius and common chord length is given by using Java programming language.

Java Program to Find Distance between Centers of Two Intersecting Circles if the Radii and Common Chord Length is Given

Before Jumping into the program directly let’s see how to Find Distance between centers of two intersecting circles if the radii and common chord length is given.

Suppose there are 2 circles named C1, C2 having radius r1, r2(given) & centers P,Q respectively

Both the circle have a common chord RS (given)

Now, you need to find the distance between the center of the two circles.

From the figure, OP is perpendicular RS
RO = OS (perpendicular bisector)
RO = RS/2 (Since, RO+OS = RS)

In triangle ROP, (using Pythagoras theorem)

H² = P² + B²
RP² = PO²+ RO²
r2² = PO² + (RS/2)²
PO² = r2² – (RS/2)²

In triangle ROO (using Pythagoras theorem)

H² = P² + B²
RQ² = QO²+ RO²
r1² = QO² + (RS/2)²
QO² = r1² – (RS/2)²

From the figure, QP = QO + OP
OP = √( r1² – (RS/2)²) + √(r2² – (RS/2)²)

Distance between the centers = √( r1² – (RS/2)²) + √(r2² – (RS/2)²)

Example:

R1 = 20

R2 = 10

AB = 7

PO = √( R1² – (AB/2)²) + √(R2² – (AB/2)²

=29.0588

Let’s see different ways to find distance between centers of two intersecting circles if the radius and common chord length is given.

By Using Static Input Value
By Using User Input Value

Method-1: Java Program to Find Distance between Centers of Two Intersecting Circles if the Radius and Common Chord Length is Given 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 C1.
Declare an double variable say ‘R2’ and assign the value to it, which holds the radius of the circle C2.
Declare an double variable say ‘AB’ and assign the value to it, which holds the length of the common chord.
Find the distance between 2 centers I.e OP using the formula √( R1² – (AB/2)²) + √(R2² – (AB/2)²)
Print the result.

Program:

import java.io.*;
class Main
{
    public static void main(String [] args)
    {
        double R1 = 20;
        double R2 =  10; 
        double AB = 7;
        // formula to find distance between center of 2 circles
        double D = Math.sqrt( R1*R1 -  (AB/2)*(AB/2)) + Math.sqrt( R2*R2 -  (AB/2)*(AB/2)) ;
        System.out.println("The distance between 2 centers is  " + D);
    }
}

Output:

The distance between 2 centers is 29.058865665112812

Method-2: Java Program to Find Distance between Centers of Two Intersecting Circles if the Radius and Common Chord Length is Given By Using User Input Value

Approach:

Declare an double variable say ‘R1’ which holds the radius of the circle C1.
Declare an double variable say ‘R2’ which holds the radius of the circle C2.
Declare an double variable say ‘AB’ which holds the length of the common chord.
Then we will take the value of “R1”, “R2”, “AB”as user input using scanner class.
Find the distance between 2 centers I.e OP using the formula √( R1² – (AB/2)²) + √(R2² – (AB/2)²)
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 length of the common chord of 2 circles");
        double AB = s.nextDouble();                     
        // formula to find distance between center of 2 circles
        double D = Math.sqrt( R1*R1 -  (AB/2)*(AB/2)) + Math.sqrt( R2*R2 -  (AB/2)*(AB/2)) ;
        System.out.println("The distance between 2 centers is  " + D);
    }
}

Output:

Enter the radius of the circle C1
20
Enter the radius of the circle C2
10
Enter the length of the common chord of 2 circles
7
The distance between 2 centers is 29.058865665112812

Interested in programming and want to excel in it by choosing the short ways. Then, practicing with the available Java Program list is mandatory.

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