检查两个给定的圆是否正交
给定两个圆心为 C1(x1，y1)和 C2(x2，y2)的圆和半径为 r1 和 r2 的，任务是检查这两个圆是否正交。 如果两条曲线的交角是直角，即它们的交点处的切线是垂直的，则称它们是正交的。
以上两个圆是正交的
例:
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
进场:
- 用距离公式求两个圆的圆心距离‘d’。
- 对于正交的圆，我们需要检查是否
r1 * r1 + r2 * r2 = d * d
- 如果是真的，那么这两个圆都是直角的。否则不行。
以下是上述方法的实现:
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 语言(一种计算机语言，尤用于创建网站)
// 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
Python 3
# 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
java 描述语言
<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.
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