CodeForces 1C Ancient Berland Circus

#include <cmath>
#include <cstdio>

using namespace std;

typedef double num;

struct vec2d {
    num x, y;

    vec2d() {}

    vec2d(num x, num y) : x(x), y(y) {}

    num len() const {
        return sqrt(x * x + y * y);
    }

    vec2d rot90() const {
        return vec2d(-y, x);
    }

    vec2d rot90(const vec2d& v) const {
        return (*this - v).rot90() + v;
    }

    vec2d operator-() const {
        return vec2d(-x, -y);
    }

    vec2d operator+(const vec2d& v) const {
        return vec2d(x + v.x, y + v.y);
    }

    vec2d operator-(const vec2d& v) const {
        return vec2d(x - v.x, y - v.y);
    }

    vec2d operator+=(const vec2d& v) {
        x += v.x;
        y += v.y;
        return *this;
    }

    vec2d operator-=(const vec2d& v) {
        x -= v.x;
        y -= v.y;
        return *this;
    }

    vec2d operator*(num a) const {
        return vec2d(x * a, y * a);
    }

    vec2d operator/(num a) const {
        return vec2d(x / a, y / a);
    }

    num operator^(const vec2d& v) const {
        return x * v.x + y * v.y;
    }

    num operator*(const vec2d& v) const {
        return x * v.y - y * v.x;
    }

    friend vec2d operator*(num a, const vec2d& v) {
        return vec2d(a * v.x, a * v.y);
    }

    num angle(vec2d u, vec2d v) const {
        u -= *this;
        v -= *this;
        return acos((u / u.len()) ^ (v / v.len()));
    }

    friend vec2d intersect(const vec2d& p1, const vec2d& p2, const vec2d& q1, const vec2d& q2) {
        num a1 = (q1 - p1) * (q2 - q1), a2 = (p2 - q1) * (q2 - p2);
        return (p2 - p1) * a1 / (a1 + a2) + p1;
    }
};

const num EPS = 1e-5, PI2 = 6.2831853072;

int main() {
    vec2d a, b, c, mid1, mid2, anc1, anc2, center;
    scanf("%lf%lf%lf%lf%lf%lf", &a.x, &a.y, &b.x, &b.y, &c.x, &c.y);
    mid1 = (a + b) / 2;
    anc1 = b.rot90(mid1);
    mid2 = (b + c) / 2;
    anc2 = c.rot90(mid2);
    center = intersect(mid1, anc1, mid2, anc2);
    for (int n = 3; n <= 100; ++n) {
        num alpha = PI2 / n, t;
        t = center.angle(a, b) / alpha;
        if (fabs(t - round(t)) > EPS)
            continue;
        t = center.angle(b, c) / alpha;
        if (fabs(t - round(t)) > EPS)
            continue;
        num r = (center - a).len();
        printf("%.9lf\n", r * r * n * sin(alpha) / 2);
        break;
    }
    return 0;
}