Problem:
Score : 500 points

Problem Statement

#nck {
width: 30px;
height: auto;
}

Snuke received a triangle as a birthday present.
The coordinates of the three vertices were (x_1, y_1), (x_2, y_2), and (x_3, y_3).

He wants to draw two circles with the same radius inside the triangle such that the two circles do not overlap (but they may touch).
Compute the maximum possible radius of the circles.

Constraints

0 ≤ x_i, y_i ≤ 1000

The coordinates are integers.

The three points are not on the same line.

Input

The input is given from Standard Input in the following format:

x_1 y_1
x_2 y_2
x_3 y_3

Output

Print the maximum possible radius of the circles.
The absolute error or the relative error must be at most 10^{-9}.

Sample Input 1

0 0
1 1
2 0

Sample Output 1

0.292893218813

Sample Input 2

3 1
1 5
4 9

Sample Output 2

0.889055514217

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<iostream>
#include<iomanip>
#include<vector>
#include<map>
#include<set>
#include<algorithm>
#include<numeric>
#include<limits>
#include<bitset>
#include<functional>
#include<type_traits>
#include<queue>
#include<stack>
#include<array>
#include<random>
#include<utility>

#include<boost/multi_array.hpp>
#include<boost/optional.hpp>
#include<boost/range/irange.hpp>
#include<boost/range/algorithm.hpp>
#include<boost/range/adaptors.hpp>
#include<boost/range/numeric.hpp>

#ifdef _MSC_FULL_VER
#include"randomizer.hpp"
#include"debug_print.hpp"
#endif

#include<cstdlib>
#include<ctime>

namespace lib
{
	template<class T>using pair = std::pair<T, T>;
	template<class T>constexpr T pow(T base, std::uint64_t p)
	{
		T ret = T(1);
		for (std::uint64_t i = 0; i <= 63; ++i)
		{
			if (((1ull << i) & p) != 0)
			{
				ret *= base;
			}
			base *= base;
		}
		return ret;
	}
	template<class T>using p_queue = std::priority_queue<T, std::vector<T>, std::greater<>>;

	struct union_find
	{
		std::vector<int> upper;
		union_find(std::size_t size):upper(size, -1) {}

		int group(int index)
		{
			if (upper[index] == -1)
			{
				return index;
			}
			else
			{
				return upper[index] = group(upper[index]);
			}
		}

		bool merge(int x, int y)
		{
			auto gx = group(x);
			auto gy = group(y);
			if (gx != gy)
			{
				upper[gx] = gy;
				return true;
			}
			return false;
		}

		auto get()
		{
			std::map<int, std::set<int>> ret;
			for (int i = 0; i < upper.size(); ++i)
			{
				ret[group(i)].emplace(i);
			}
			return ret;
		}

		auto tops()
		{
			std::set<int> ret;
			for (int i = 0; i < upper.size(); ++i)
			{
				ret.emplace(group(i));
			}
			return ret;
		}

		bool is_same_group(int x, int y)
		{
			return group(x) == group(y);
		}
	};
}

namespace out
{
	namespace detail
	{
		template<class>struct void_out
		{
			typedef void type;
		};
		template<class T>auto write(std::ostream& ost, T const& val)
			->typename void_out<decltype(ost << val)>::type
		{
			ost << val;
		}
		template<class T, class... Ts>void write(std::ostream& ost, T const& val, Ts const&... nexts)
		{
			write(ost, val);
			ost << " ";
			write(ost, nexts...);
		}
	}
	void write_line()
	{
		std::cout << std::endl;
	}
	template<class...Ts>void write_line(Ts const&... args)
	{
		detail::write(std::cout, args...);
		write_line();
	}
	template<class Range>void write_range(Range const& rng)
	{
		for (auto const& v : rng)
		{
			write_line(v);
		}
	}
}

namespace adaptor = boost::adaptors;

void Main()
{
	double x[3], y[3];
	std::cin >> x[0] >> y[0];
	std::cin >> x[1] >> y[1];
	std::cin >> x[2] >> y[2];
	auto ax = x[1] - x[0];
	auto bx = x[2] - x[1];
	auto cx = x[0] - x[2];
	auto ay = y[1] - y[0];
	auto by = y[2] - y[1];
	auto cy = y[0] - y[2];
	auto a = std::sqrt(ax * ax + ay * ay);
	auto b = std::sqrt(bx * bx + by * by);
	auto c = std::sqrt(cx * cx + cy * cy);
	auto s = (a + b + c) / 2;
	auto S = std::sqrt(s*(s - a)*(s - b)*(s - c));
	auto R = S / s;
	auto max = std::max({ a,b,c });
	out::write_line(max*R / (max + 2 * R));
}

int main()
{
	std::cin.tie(nullptr);
	std::cin.sync_with_stdio(false);
	std::cout << std::fixed << std::setprecision(15);
	Main();
}