内接圆的正方形中最大的三角形

原文:https://www . geesforgeks . org/big-reuleaux-正方形内接三角形/圆形内接三角形/

这里给定的是一个半径为 r 的圆，圆上刻有一个正方形，正方形上又刻有一个三角形。任务是找到这个 reuleaux 三角形的最大可能面积。 例:

Input: r = 6
Output: 50.7434

Input: r = 11
Output: 170.554

走近:从图中可以很清楚的看到，如果广场的一边是 a ，那么

aⅰ2 = 2r a =【2r】

另外，在重入三角形中， h = a = √2r ，请参考正方形内最大的重入三角形。 所以，Reuleaux 三角的区域是，a = 0.70477h^2 = 0.704772*r^2

C++

// C++ Program to find the biggest Reuleaux
// triangle inscribed within in a square which
// in turn is inscribed within a circle
#include <bits/stdc++.h>
using namespace std;

// Function to find the Area
// of the Reuleaux triangle
float ReuleauxArea(float r)
{

    // radius cannot be negative
    if (r < 0)
        return -1;

    // Area of the Reuleaux triangle
    float A = 0.70477 * 2 * pow(r, 2);

    return A;
}

// Driver code
int main()
{
    float r = 6;
    cout << ReuleauxArea(r) << endl;
    return 0;
}

Java 语言(一种计算机语言，尤用于创建网站)

// Java Program to find the biggest Reuleaux
// triangle inscribed within in a square which
// in turn is inscribed within a circle
import java.util.*;

class GFG
{

// Function to find the Area
// of the Reuleaux triangle
static double ReuleauxArea(double r)
{

    // radius cannot be negative
    if (r < 0)
        return -1;

    // Area of the Reuleaux triangle
    double A = 0.70477 * 2 * Math.pow(r, 2);

    return A;
}

// Driver code
public static void main(String args[])
{
    double r = 6;
    System.out.println(ReuleauxArea(r));

}
}
// This code is contributed by
// Surendra_Gangwar

Python 3

# Python3 Program to find the biggest
# Reuleaux triangle inscribed within
# in a square which in turn is inscribed
# within a circle
import math as mt

# Function to find the Area
# of the Reuleaux triangle
def ReuleauxArea(r):

    # radius cannot be negative
    if (r < 0):
        return -1

    # Area of the Reuleaux triangle
    A = 0.70477 * 2 * pow(r, 2)

    return A

# Driver code
r = 6
print(ReuleauxArea(r))

# This code is contributed by
# Mohit kumar 29

C

// C# Program to find the biggest Reuleaux
// triangle inscribed within in a square which
// in turn is inscribed within a circle
using System;

class GFG
{

// Function to find the Area
// of the Reuleaux triangle
static double ReuleauxArea(double r)
{

    // radius cannot be negative
    if (r < 0)
        return -1;

    // Area of the Reuleaux triangle
    double A = 0.70477 * 2 * Math.Pow(r, 2);

    return A;
}

// Driver code
public static void Main()
{
    double r = 6;
    Console.WriteLine(ReuleauxArea(r));
}
}

// This code is contributed by
// shs..

服务器端编程语言（Professional Hypertext Preprocessor 的缩写）

<?php
// PHP Program to find the biggest Reuleaux
// triangle inscribed within in a square
// which in turn is inscribed within a circle

// Function to find the Area of the
// Reuleaux triangle
function ReuleauxArea($r)
{

    // radius cannot be negative
    if ($r < 0)
        return -1;

    // Area of the Reuleaux triangle
    $A = 0.70477 * 2 * pow($r, 2);

    return $A;
}

// Driver code
$r = 6;
echo ReuleauxArea($r) . "\n";

// This code is contributed by ita_c
?>

java 描述语言

<script>
// javascript Program to find the biggest Reuleaux
// triangle inscribed within in a square which
// in turn is inscribed within a circle

// Function to find the Area
// of the Reuleaux triangle
function ReuleauxArea(r)
{

    // radius cannot be negative
    if (r < 0)
        return -1;

    // Area of the Reuleaux triangle
    var A = 0.70477 * 2 * Math.pow(r, 2);

    return A;
}

// Driver code

var r = 6;
document.write(ReuleauxArea(r));

// This code contributed by Princi Singh
</script>

Output: 

50.7434

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