# 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 = 2
Output: 3.14

Input: R = 8
Output: 50.24
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: Let R be the radius of the semicircle

1. 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.
2. So, if the radius of the semi-circle is R, then the diameter of the largest inscribed circle will be R.
3. Hence the radius of the inscribed circle must be R/2
4. Therefore the area of the largest circle will be
```Area of circle = pi*Radius2
= 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 ` `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 `

Output:

```3.14
```

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