给定半径给定的两个圆,它们的中心相距给定的距离,使得这些圆在两点相交。任务是找到圆之间的直接公切线的长度。
例子:
Input: r1 = 4, r2 = 6, d = 3
Output: 2.23607
Input: r1 = 14, r2 = 43, d = 35
Output: 19.5959
方法:
- 设圆的半径分别为r1和r2 。
- 让中心之间的距离为d 个单位。
- 画一条线 OR 平行于 PQ
- 角度 OPQ = 90 度
角度 O’QP = 90 度
{ 连接圆心和接触点的线与切线成 90 度角 }
- 角度 OPQ + 角度 O’QP = 180 度
操作||二维码
- 由于对边平行且内角为90°,所以OPQR是一个矩形。
- 所以OP = QR = r1 和 PQ = OR = d
- 在三角形 OO’R
角度 ORO’ = 90
根据毕达哥拉斯定理
OR^2 + O’R^2 = (OO’^2)
或^2 + (r1-r2)^2 = d^2
- 所以, OR^2= d^2-(r1-r2)^2
OR = √{d^2-(r1-r2)^2}
下面是上述方法的实现:
C++
// C++ program to find
// the length of the direct
// common tangent between two circles
// which intersect each other
#include
using namespace std;
// Function to find the length of the direct common tangent
void lengtang(double r1, double r2, double d)
{
cout << "The length of the direct"
<<" common tangent is "
<< sqrt(pow(d, 2) - pow((r1 - r2), 2))
<< endl;
}
// Driver code
int main()
{
double r1 = 4, r2 = 6, d = 3;
lengtang(r1, r2, d);
return 0;
}
Java
// Java program to find
// the length of the direct
// common tangent between two circles
// which intersect each other
class GFG
{
// Function to find the length of
// the direct common tangent
static void lengtang(double r1, double r2, double d)
{
System.out.println("The length of the direct"
+ " common tangent is "
+ (Math.sqrt(Math.pow(d, 2) -
Math.pow((r1 - r2), 2))));
}
// Driver code
public static void main(String[] args)
{
double r1 = 4, r2 = 6, d = 3;
lengtang(r1, r2, d);
}
}
/* This code contributed by PrinciRaj1992 */
Python3
# Python program to find
# the length of the direct
# common tangent between two circles
# which intersect each other
# Function to find the length of
# the direct common tangent
def lengtang(r1, r2, d):
print("The length of the direct common tangent is "
,((d** 2) - ((r1 - r2)** 2))**(1/2));
# Driver code
r1 = 4; r2 = 6; d = 3;
lengtang(r1, r2, d);
# This code has been contributed by 29AjayKumar
C#
// C# program to find
// the length of the direct
// common tangent between two circles
// which intersect each other
using System;
class GFG
{
// Function to find the length of
// the direct common tangent
static void lengtang(double r1, double r2, double d)
{
Console.WriteLine("The length of the direct"
+ " common tangent is "
+ (Math.Sqrt(Math.Pow(d, 2) -
Math.Pow((r1 - r2), 2))));
}
// Driver code
public static void Main(String[] args)
{
double r1 = 4, r2 = 6, d = 3;
lengtang(r1, r2, d);
}
}
/* This code contributed by PrinciRaj1992 */
PHP
Javascript
输出:
The length of the direct common tangent is 2.23607
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