#include<cstdio>#include<cstring>#include<cstdlib>#include<cmath>#include<algorithm>#include<string>#include<map>#include<set>#include<iostream>#include<vector>#include<queue>using namespace std;#define sz(v) ((int)(v).size())#define rep(i, n) for (int i = 0; i < (n); ++i)#define repf(i, a, b) for (int i = (a); i <= (b); ++i)#define repd(i, a, b) for (int i = (a); i >= (b); --i)#define clr(x) memset(x,0,sizeof(x))#define clrs( x , y ) memset(x,y,sizeof(x))#define out(x) printf(#x" %dn", x)#define sqr(x) ((x) * (x))typedef long long lint;const int maxint = -1u>>1;const double pi = acos(-1.0);const double eps = 1e-8;int sgn(const double &x) { return (x > eps) - (x < -eps); }struct point { double x, y; point (double _x = 0, double _y = 0) : x(_x), y(_y) { } double operator * (const point &p) const { return (x * p.y) - (y * p.x); } point operator - (const point &p) const { return point(x - p.x, y - p.y); } point operator + (const point &p) const { return point(x + p.x, y + p.y); } void output() { printf("%.3f %.3fn", x, y); }};point operator * (const double &l, const point &p) { return point(l * p.x, l * p.y);}vector<point> p;void gao(point u, point v, double r) { double a = sqr(v.x - u.x) + sqr(v.y - u.y); double b = 2 * ((v.x - u.x) * u.x + (v.y - u.y) * u.y); double c = sqr(u.x) + sqr(u.y) - sqr(r); double det = b * b - 4 * a * c; p.push_back(u); if (det < 0) { return; } double t1 = (-b + sqrt(det)) / 2 / a; double t2 = (-b - sqrt(det)) / 2 / a; if (t1 > t2) swap(t1, t2); if (sgn(t1) > 0 && sgn(t1 - 1) < 0) { p.push_back(u + t1 * (v - u)); } if (sgn(t2) > 0 && sgn(t2 - 1) < 0 && sgn(t1 - t2) != 0) { p.push_back(u + t2 * (v - u)); } }double tri(point a, point b) { return abs( (a * b) / 2 );}double sec(point a, point b, double r) { double ang1 = atan2(a.y, a.x); double ang2 = atan2(b.y, b.x); if (ang1 < 0) ang1 = 2 * pi + ang1; if (ang2 < 0) ang2 = 2 * pi + ang2; double dang = abs(ang2 - ang1); if (dang > pi) dang = 2 * pi - dang; return r * r * dang / 2;}int main() { bool blank = false; double x, y, r, x1, y1, x2, y2; while (scanf("%lf%lf%lf", &x, &y, &r) == 3) { if (blank) puts(""); blank = 1; scanf("%lf%lf%lf%lf", &x1, &y1, &x2, &y2); x1 -= x; y1 -= y; x2 -= x; y2 -= y; p.clear(); gao(point(x1, y1), point(x1, y2), r); gao(point(x1, y2), point(x2, y2), r); gao(point(x2, y2), point(x2, y1), r); gao(point(x2, y1), point(x1, y1), r); double ans = 0; p.push_back(p.front()); rep (i, sz(p) - 1) { if (sgn( hypot((p[i].x + p[i + 1].x) / 2, (p[i].y + p[i + 1].y) / 2) - r) >= 0) { ans += sgn(p[i] * p[i + 1]) * sec(p[i], p[i + 1], r); } else { ans += sgn(p[i] * p[i + 1]) * tri(p[i], p[i + 1]); } } printf("%.11fn", abs(ans)); } return 0;}
