给定三角形的顶点和边长。一个圆内接于一个三角形。任务是找到三角形的中心。
例子:
Input: A(2, 2), B(1, 1), C(3, 1)
and AB = 2, BC = 1, AC = 1
Output: (2, 1.5)
Input: A(3, 3), B(1, 2), C(2, 2)
and AB = 3, BC = 2, AC = 2
Output: (2.5, 2.83)
方法:
- 与三角形边相接的圆心称为内心。
- 假设三角形的顶点是 A(x1, y1)、B(x2, y2) 和 C(x3, y3)。
- 让边 AB = a, BC = b, AC = c 那么中心的坐标由公式给出:
下面是上述方法的实现:
C++
// C++ program to find the
// incenter of a triangle
#include
using namespace std;
// Driver code
int main()
{
// coordinate of the vertices
float x1 = 2, x2 = 1, x3 = 3;
float y1 = 2, y2 = 1, y3 = 1;
float a = 2, b = 1, c = 1;
// Formula to calculate in-center
float x = (a * x1 + b *
x2 + c * x3) / (a + b + c);
float y = (a * y1 + b *
y2 + c * y3) / (a + b + c);
// System.out.print(setprecision(3));
cout << "Incenter = "
<< "(" << x << ", " << y << ")";
return 0;
}
// This code is contributed by 29AjayKumar
Java
// Java program to find the
// incenter of a triangle
import java.util.*;
import java.lang.*;
class GFG {
// Driver code
public static void main(String args[])
{
// coordinate of the vertices
float x1 = 2, x2 = 1, x3 = 3;
float y1 = 2, y2 = 1, y3 = 1;
float a = 2, b = 1, c = 1;
// Formula to calculate in-center
float x
= (a * x1 + b * x2 + c * x3) / (a + b + c);
float y
= (a * y1 + b * y2 + c * y3) / (a + b + c);
// System.out.print(setprecision(3));
System.out.println("Incenter= "
+ "(" + x + ", " + y + ")");
}
}
Python3
# Python3 program to find the
# incenter of a triangle
# Driver code
# coordinate of the vertices
x1 = 2; x2 = 1; x3 = 3;
y1 = 2; y2 = 1; y3 = 1;
a = 2; b = 1; c = 1;
# Formula to calculate in-center
x = (a * x1 + b * x2 + c * x3) / (a + b + c);
y = (a * y1 + b * y2 + c * y3) / (a + b + c);
# System.out.print(setprecision(3));
print("Incenter = (", x, ",", y, ")");
# This code is contributed
# by Akanksha Rai
C#
// C# program to find the
// incenter of a triangle
using System;
class GFG
{
// Driver code
public static void Main()
{
// coordinate of the vertices
float x1 = 2, x2 = 1, x3 = 3;
float y1 = 2, y2 = 1, y3 = 1;
float a = 2, b = 1, c = 1;
// Formula to calculate in-center
float x
= (a * x1 + b * x2 + c * x3) / (a + b + c);
float y
= (a * y1 + b * y2 + c * y3) / (a + b + c);
// System.out.print(setprecision(3));
Console.WriteLine("Incenter= "
+ "(" + x + ", " + y + ")");
}
}
// This code is contributed by vt_m.
Javascript
输出:
Incenter= (2.0, 1.5)
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