# Area of largest Circle that can be inscribed in a SemiCircle

Given a semicircle with radius **R**, the task is to find the area of the largest circle that can be inscribed in the semicircle.**Examples:**

Input:R = 2Output:3.14Input:R = 8Output:50.24

**Approach**: Let **R** be the radius of the semicircle

- For Largest circle that can be inscribed in this semicircle, the diameter of the circle must be equal to the radius of the semi-circle.

- So, if the radius of the semi-circle is
**R**, then the diameter of the largest inscribed circle will be**R**. - Hence the radius of the inscribed circle must be
**R/2** - Therefore the area of the largest circle will be

Area of circle = pi*Radius^{2}= pi*(R/2)^{2}since the radius of largest circle is R/2 where R is the radius of the semicircle

Below is the implementation of the above approach:

## C++

`// C++ Program to find the biggest circle` `// which can be inscribed within the semicircle` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find the area` `// of the circle` `float` `circlearea(` `float` `R)` `{` ` ` `// Radius cannot be negative` ` ` `if` `(R < 0)` ` ` `return` `-1;` ` ` `// Area of the largest circle` ` ` `float` `a = 3.14 * R * R / 4;` ` ` `return` `a;` `}` `// Driver code` `int` `main()` `{` ` ` `float` `R = 2;` ` ` `cout << circlearea(R) << endl;` ` ` `return` `0;` `}` |

## Java

`// Java Program to find the biggest circle` `// which can be inscribed within the semicircle` `class` `GFG` `{` ` ` ` ` `// Function to find the area` ` ` `// of the circle` ` ` `static` `float` `circlearea(` `float` `R)` ` ` `{` ` ` ` ` `// Radius cannot be negative` ` ` `if` `(R < ` `0` `)` ` ` `return` `-` `1` `;` ` ` ` ` `// Area of the largest circle` ` ` `float` `a = (` `float` `)((` `3.14` `* R * R) / ` `4` `);` ` ` ` ` `return` `a;` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `main (String[] args)` ` ` `{` ` ` `float` `R = ` `2` `;` ` ` `System.out.println(circlearea(R));` ` ` `}` `}` `// This code is contributed by AnkitRai01` |

## Python3

`# Python3 Program to find the biggest circle` `# which can be inscribed within the semicircle` `# Function to find the area` `# of the circle` `def` `circlearea(R) :` ` ` `# Radius cannot be negative` ` ` `if` `(R < ` `0` `) :` ` ` `return` `-` `1` `;` ` ` `# Area of the largest circle` ` ` `a ` `=` `(` `3.14` `*` `R ` `*` `R) ` `/` `4` `;` ` ` `return` `a;` `# Driver code` `if` `__name__ ` `=` `=` `"__main__"` `:` ` ` `R ` `=` `2` `;` ` ` `print` `(circlearea(R)) ;` ` ` `# This code is contributed by AnkitRai01` |

## C#

`// C# Program to find the biggest circle` `// which can be inscribed within the semicircle` `using` `System;` `class` `GFG` `{` ` ` ` ` `// Function to find the area` ` ` `// of the circle` ` ` `static` `float` `circlearea(` `float` `R)` ` ` `{` ` ` ` ` `// Radius cannot be negative` ` ` `if` `(R < 0)` ` ` `return` `-1;` ` ` ` ` `// Area of the largest circle` ` ` `float` `a = (` `float` `)((3.14 * R * R) / 4);` ` ` ` ` `return` `a;` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `Main (` `string` `[] args)` ` ` `{` ` ` `float` `R = 2;` ` ` `Console.WriteLine(circlearea(R));` ` ` `}` `}` `// This code is contributed by AnkitRai01` |

## Javascript

`<script>` `// Javascript Program to find the biggest circle` `// which can be inscribed within the semicircle` `// Function to find the area` `// of the circle` `function` `circlearea(R)` `{` ` ` `// Radius cannot be negative` ` ` `if` `(R < 0)` ` ` `return` `-1;` ` ` `// Area of the largest circle` ` ` `var` `a = 3.14 * R * R / 4;` ` ` `return` `a;` `}` `// Driver code` `var` `R = 2;` `document.write(circlearea(R));` `// This code is contributed by rutvik_56.` `</script>` |

**Output:**

3.14

**Time Complexity**: O(1)

**Auxiliary Space:** O(1)