A.cpp

#include <bits/stdc++.h>
#define FOR(i,a,b) for(int i=(a),_b=(b); i<=_b; ++i)
#define FORD(i,a,b) for(int i=(a),_b=(b); i>=_b; --i)
#define REP(i,a) for(int i=0,_a=(a); i < _a; ++i)

#define DEBUG(X) { cout << #X << " = " << X << endl; }
#define PR(A,n)  { cout << #A << " = "; FOR(_,1,n) cout << A[_] << ' '; cout << endl; }
#define PR0(A,n) { cout << #A << " = "; REP(_,n) cout << A[_] << ' '; cout << endl; }

#define sqr(x) ((x) * (x))
#define ll long long
#define SZ(x) ((int) (x).size())
#define D double
using namespace std;

#define EPS 1e-6
inline int cmp(double a, double b) {
    return (a < b - EPS) ? -1 : ((a > b + EPS) ? 1 : 0);
}

struct Point {
    double x, y;
    Point(double x = 0.0, double y = 0.0) : x(x), y(y) {}

    Point operator + (Point a) { return Point(x+a.x, y+a.y); }
    Point operator - (Point a) { return Point(x-a.x, y-a.y); }
    Point operator * (double k) { return Point(x*k, y*k); }
    Point operator / (double k) { return Point(x/k, y/k); }

    double operator * (Point a) { return x*a.x + y*a.y; } // dot product
    double operator % (Point a) { return x*a.y - y*a.x; } // cross product

    int cmp(Point q) const { if (int t = ::cmp(x,q.x)) return t; return ::cmp(y,q.y); }

    #define Comp(x) bool operator x (Point q) const { return cmp(q) x 0; }
    Comp(>) Comp(<) Comp(==) Comp(>=) Comp(<=) Comp(!=)
    #undef Comp

    Point conj() { return Point(x, -y); }
    double norm() { return x*x + y*y; }

    double len() { return sqrt(norm()); }

    Point rotate(double alpha) {
        double cosa = cos(alpha), sina = sin(alpha);
        return Point(x * cosa - y * sina, x * sina + y * cosa);
    }
    void read() {
        int t;
        scanf("%d", &t); x = t;
        scanf("%d", &t); y = t;
    }
} a[100111];

double distToLine(Point p, Point a, Point b, Point &c) {
    Point ap = p - a, ab = b - a;
    double u = (ap * ab) / ab.norm();
    c = a + (ab * u);
    return (p-c).len();
}
double distToLineSegment(Point p, Point a, Point b, Point &c) {
    Point ap = p - a, ab = b - a;
    double u = (ap * ab) / ab.norm();
    if (u < 0.0) {
        c = Point(a.x, a.y);
        return (p - a).len();
    }
    if (u > 1.0) {
        c = Point(b.x, b.y);
        return (p - b).len();
    }
    return distToLine(p, a, b, c);
}

int main() {
    int n;
    while (scanf("%d", &n) == 1) {
        Point P;
        P.read();
        FOR(i,1,n) {
            a[i].read();
            a[i] = a[i] - P;
        }
        a[0] = a[n];
        a[n+1] = a[1];

        D min_dist = 1e20, max_dist = -1;
        if (min_dist < 0) min_dist = 0;

        Point O(0, 0);
        Point t;
        FOR(i,1,n) {
            min_dist = min(min_dist, a[i].len());
            max_dist = max(max_dist, a[i].len());

            min_dist = min(min_dist, distToLineSegment(O, a[i], a[i+1], t));
        }
        cout << (fixed) << setprecision(12) << acos(-1.0) * (sqr(max_dist) - sqr(min_dist)) << endl;
    }
}