Given are two circles with their centres C1(x1, y1) and C2(x2, y2) and radius r1 and r2, the task is to check if both the circles are orthogonal or not.
Two curves are said to be orthogonal if their angle of intersection is a right angle i.e the tangents at their point of intersection are perpendicular.
Examples:
Input: C1(4, 3), C2(0, 1), r1 = 2, r2 = 4 Output: Yes Input: C1(4, 3), C2(1, 2), r1 = 2, r2 = 2 Output: No
Approach:
- Find the distance between the centres of two circles ‘d’ with distance formula.
- For the circles to be orthogonal we need to check if
r1 * r1 + r2 * r2 = d * d
- If it is true, then both the circles are orthagonal. Else not.
Below is the implementation of the above approach:
C++
// C++ program to check if two // circles are orthogonal or not #include <bits/stdc++.h> using namespace std;
// Function to Check if the given // circles are orthogonal bool orthogonality( int x1, int y1, int x2,
int y2, int r1, int r2)
{ // calculating the square
// of the distance between C1 and C2
int dsquare = (x1 - x2) * (x1 - x2)
+ (y1 - y2) * (y1 - y2);
// Check if the given
// circles are orthogonal
if (dsquare == r1 * r1 + r2 * r2)
return true ;
else
return false ;
} // Driver code int main()
{ int x1 = 4, y1 = 3;
int x2 = 0, y2 = 1;
int r1 = 2, r2 = 4;
bool f = orthogonality(x1, y1, x2,
y2, r1, r2);
if (f)
cout << "Given circles are"
<< " orthogonal." ;
else
cout << "Given circles are"
<< " not orthogonal." ;
return 0;
} |
Java
// Java program to check if two // circ import java.util.*;
import java.lang.*;
import java.io.*;
class GFG
{ // Function to Check if the given
// circles are orthogonal
public static boolean orthogonality( int x1, int y1, int x2,
int y2, int r1, int r2)
{
// calculating the square
// of the distance between C1 and C2
int dsquare = (x1 - x2) * (x1 - x2) +
(y1 - y2) * (y1 - y2);
// Check if the given
// circles are orthogonal
if (dsquare == r1 * r1 + r2 * r2)
return true ;
else
return false ;
}
// Driver Code
public static void main(String[] args) throws java.lang.Exception
{
int x1 = 4 , y1 = 3 ;
int x2 = 0 , y2 = 1 ;
int r1 = 2 , r2 = 4 ;
boolean f = orthogonality(x1, y1, x2, y2, r1, r2);
if (f)
System.out.println( "Given circles are orthogonal." );
else
System.out.println( "Given circles are not orthogonal." );
}
} // This code is contributed by ashutosh450 |
Python3
# Python3 program to check if two # circles are orthogonal or not # Function to Check if the given # circles are orthogonal def orthogonality(x1, y1, x2, y2, r1, r2):
# calculating the square
# of the distance between C1 and C2
dsquare = (x1 - x2) * (x1 - x2) + \
(y1 - y2) * (y1 - y2);
# Check if the given
# circles are orthogonal
if (dsquare = = r1 * r1 + r2 * r2):
return True
else :
return False
# Driver code x1, y1 = 4 , 3
x2, y2 = 0 , 1
r1, r2 = 2 , 4
f = orthogonality(x1, y1, x2, y2, r1, r2)
if (f):
print ( "Given circles are orthogonal." )
else :
print ( "Given circles are not orthogonal." )
# This code is contributed by Mohit Kumar |
C#
// C# implementation for above program using System;
class GFG
{ // Function to Check if the given
// circles are orthogonal
public static bool orthogonality( int x1, int y1, int x2,
int y2, int r1, int r2)
{
// calculating the square
// of the distance between C1 and C2
int dsquare = (x1 - x2) * (x1 - x2) +
(y1 - y2) * (y1 - y2);
// Check if the given
// circles are orthogonal
if (dsquare == r1 * r1 + r2 * r2)
return true ;
else
return false ;
}
// Driver Code
public static void Main()
{
int x1 = 4, y1 = 3;
int x2 = 0, y2 = 1;
int r1 = 2, r2 = 4;
bool f = orthogonality(x1, y1, x2, y2, r1, r2);
if (f)
Console.WriteLine( "Given circles are orthogonal." );
else
Console.WriteLine( "Given circles are not orthogonal." );
}
} // This code is contributed by AnkitRai01 |
Javascript
<script> // Javascript program to check if two
// circles are orthogonal or not
// Function to Check if the given
// circles are orthogonal
function orthogonality(x1, y1, x2, y2, r1, r2)
{
// calculating the square
// of the distance between C1 and C2
let dsquare = (x1 - x2) * (x1 - x2)
+ (y1 - y2) * (y1 - y2);
// Check if the given
// circles are orthogonal
if (dsquare == r1 * r1 + r2 * r2)
return true ;
else
return false ;
}
// Driver code
let x1 = 4, y1 = 3;
let x2 = 0, y2 = 1;
let r1 = 2, r2 = 4;
let f = orthogonality(x1, y1, x2,
y2, r1, r2);
if (f)
document.write( "Given circles are orthogonal." );
else
document.write( "Given circles are not orthogonal." );
// This code is contributed by divyesh072019. </script> |
Output:
Given circles are orthogonal.
Time Complexity: O(1)
Auxiliary Space: O(1)
Recommended Articles