Language: C++

#include<bits/stdc++.h>
#include<boost/multiprecision/cpp_int.hpp>
#include<boost/rational.hpp>
#include<boost/multiprecision/cpp_dec_float.hpp>
namespace fast {
    // fast I/O by rsk0315 (update: 2019-10-14 16:56:15).
    // This version supports only integer inputs/outputs, single character
    // outputs, and string literal outputs.
    static size_t constexpr buf_size = 1 << 17;
    static size_t constexpr margin = 1;
    static char inbuf[buf_size + margin] = {};
    static char outbuf[buf_size + margin] = {};
    static __attribute__((aligned(8))) char minibuf[32];
    static size_t constexpr int_digits = 20;  // 18446744073709551615
    static uintmax_t constexpr digit_mask = 0x3030303030303030;
    static uintmax_t constexpr first_mask = 0x00FF00FF00FF00FF;
    static uintmax_t constexpr second_mask = 0x0000FFFF0000FFFF;
    static uintmax_t constexpr third_mask = 0x00000000FFFFFFFF;
    static uintmax_t constexpr tenpow[] = {
            1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000
    };
    template <typename Tp>
    using enable_if_integral = std::enable_if<std::is_integral<Tp>::value, Tp>;

    class scanner {
        char* pos = inbuf;
        char* endpos = inbuf + buf_size;

        void M_read_from_stdin() {
            endpos = inbuf + fread(pos, 1, buf_size, stdin);
        }
        void M_reread_from_stdin() {
            ptrdiff_t len = endpos - pos;
            if (!(inbuf + len <= pos)) return;
            memcpy(inbuf, pos, len);
            char* tmp = inbuf + len;
            endpos = tmp + fread(tmp, 1, buf_size-len, stdin);
            *endpos = 0;
            pos = inbuf;
        }

    public:
        scanner() { M_read_from_stdin(); }

        template <typename Integral,
                typename enable_if_integral<Integral>::type* = nullptr>
        void scan_parallel(Integral& x) {
            // See https://qiita.com/rsk0315_h4x/items/17a9cb12e0de5fd918f4
            if (__builtin_expect(endpos <= pos + int_digits, 0))
                M_reread_from_stdin();
            bool ends = false;
            typename std::make_unsigned<Integral>::type y = 0;
            bool neg = false;
            if (std::is_signed<Integral>::value && *pos == '-') {
                neg = true;
                ++pos;
            }
            do {
                memcpy(minibuf, pos, 8);
                long c = *(long*)minibuf;
                long d = (c & digit_mask) ^ digit_mask;
                int skip = 8;
                int shift = 8;
                if (d) {
                    int ctz = __builtin_ctzl(d);
                    if (ctz == 4) break;
                    c &= (1L << (ctz-5)) - 1;
                    int discarded = (68-ctz) / 8;
                    shift -= discarded;
                    c <<= discarded * 8;
                    skip -= discarded;
                    ends = true;
                }
                c |= digit_mask;
                c ^= digit_mask;
                c = ((c >> 8) + c*10) & first_mask;
                c = ((c >> 16) + c*100) & second_mask;
                c = ((c >> 32) + c*10000) & third_mask;
                y = y*tenpow[shift] + c;
                pos += skip;
            } while (!ends);
            x = (neg? -y: y);
            ++pos;
        }

        template <typename Integral,
                typename enable_if_integral<Integral>::type* = nullptr>
        void scan_serial(Integral& x) {
            if (__builtin_expect(endpos <= pos + int_digits, 0))
                M_reread_from_stdin();
            bool neg = false;
            if (std::is_signed<Integral>::value && *pos == '-') {
                neg = true;
                ++pos;
            }
            typename std::make_unsigned<Integral>::type y = *pos-'0';
            while (*++pos >= '0') y = 10*y + *pos-'0';
            x = (neg? -y: y);
            ++pos;
        }

        template <typename Integral,
                typename enable_if_integral<Integral>::type* = nullptr>
        // Use scan_parallel(x) only when x may be too large (about 10^12).
        // Otherwise, even when x <= 10^9, scan_serial(x) may be faster.
        void scan(Integral& x) { scan_serial(x); }

        void scan_serial(std::string& s) {
            // until first whitespace
            s = "";
            do {
                char* startpos = pos;
                while (*pos > ' ') ++pos;
                s += std::string(startpos, pos);
                if (*pos != 0) {
                    ++pos;  // skip the space
                    break;
                }
                M_reread_from_stdin();
            } while (true);
        }

        void scan(std::string& s) { scan_serial(s); }
    };

    class printer {
        char* pos = outbuf;

        void M_flush_stdout() {
            fwrite(outbuf, 1, pos-outbuf, stdout);
            pos = outbuf;
        }

    public:
        printer() = default;
        ~printer() { M_flush_stdout(); }

        void print(char c) {
            if (__builtin_expect(pos + 1 >= outbuf + buf_size, 0)) M_flush_stdout();
            *pos++ = c;
        }

        template <size_t N>
        void print(char const(&s)[N]) {
            if (__builtin_expect(pos + N >= outbuf + buf_size, 0)) M_flush_stdout();
            memcpy(pos, s, N-1);
            pos += N-1;
        }

        void print(char const* s) {
            while (*s != 0) {
                *pos++ = *s++;
                if (pos == outbuf + buf_size) M_flush_stdout();
            }
        }

        template <typename Integral,
                typename enable_if_integral<Integral>::type* = nullptr>
        void print(Integral x) {
            if (__builtin_expect(pos + int_digits >= outbuf + buf_size, 0))
                M_flush_stdout();
            if (x == 0) {
                *pos++ = '0';
                return;
            }
            if (x < 0) {
                *pos++ = '-';
                if (__builtin_expect(x == std::numeric_limits<Integral>::min(), 0)) {
                    switch (sizeof x) {
                        case 2: print("32768"); return;
                        case 4: print("2147483648"); return;
                        case 8: print("9223372036854775808"); return;
                    }
                }
                x = -x;
            }
            char* mp = minibuf + sizeof minibuf;
            *--mp = x % 10 + '0';
            size_t len = 1;
            typename std::make_unsigned<Integral>::type y = x / 10;
            while (y > 0) {
                *--mp = y % 10 + '0';
                y /= 10;
                ++len;
            }
            memcpy(pos, mp, len);
            pos += len;
        }

        template <typename Tp>
        void println(Tp const& x) { print(x), print('\n'); }
    };
} // fast::

fast::scanner in;
fast::printer out;

// thank you ebi-chan!

int main(){
    using namespace std;
    using real = boost::rational<boost::multiprecision::cpp_int>;
    using point = complex<real>;
    using circle = pair<point, real>;
    unsigned long N;
    in.scan(N);
    vector<point> p(N);
    for(auto& i : p){
        unsigned long im, re;
        in.scan(im);
        in.scan(re);
        i.imag(real(im));
        i.real(real(re));
    }
    {
        mt19937_64 mt{random_device{}()};
        shuffle(p.begin(), p.end(), mt);
    }
    const auto& circle_from_diameter = [](const point& a, const point& b) -> circle {
        auto center = (a + b) / real(2);
        return {center, norm(a - center)};
    };
    const auto& circle_from_triangle = [](const point& a, const point& b, const point& c) -> circle {
        if(((a - b) / (a - c)).imag() == 0)return circle{};
        auto center = ((a - b) * norm(c) + (b - c) * norm(a) + (c - a) * norm(b)) / ((a - b) * conj(c) + (b - c) * conj(a) + (c - a) * conj(b));
        return {center, norm(a - center)};
    };
    const auto& is_included = [](const circle& c, const point& a) -> bool {
        return norm(a - c.first) <= c.second;
    };
    const auto& is_all_include = [&p, &is_included](const circle& c) -> bool {
        return all_of(p.begin(), p.end(), [&c, &is_included](const point& a){return is_included(c, a);});
    };
    auto c = circle_from_diameter(p[0], p[1]);
    for(unsigned long i{2}; i < N; ++i)if(!is_included(c, p[i])){
        c = circle_from_diameter(p[0], p[i]);
        for(unsigned long j{1}; j < i; ++j)if(!is_included(c, p[j])){
            c = circle_from_diameter(p[i], p[j]);
            for(unsigned long k{0}; k < j; ++k)if(!is_included(c, p[k]))c = circle_from_triangle(p[i], p[j], p[k]);
        }
    }
    boost::multiprecision::cpp_dec_float_100 t = boost::multiprecision::sqrt(boost::rational_cast<boost::multiprecision::cpp_dec_float_100>(c.second));
    out.println(t.str());
    return 0;
}

Compiler output:
a.cc:2:9: fatal error: boost/multiprecision/cpp_int.hpp: No such file or directory
    2 | #include<boost/multiprecision/cpp_int.hpp>
      |         ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
compilation terminated.