每条线段与原点连起来求在圆内的有向面积，然后输出之前绝对值一下。

求三角形在圆内的面积，都在圆内，直接三角形面积，都在圆外且无交点，直接扇形面积，如果一点在圆内一点在圆外的话，求一个扇形一个三角形，两点在圆外但有2个交点，则求2个扇形中间一个三角形的面积。

使用点积解方程求线段与圆的交点过不了这题，不知道为何，但用上交小红书的解方程模板就可以

#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<vector>
#define maxl 510
#define eps 1e-10
const double pi=acos(-1.0);
using namespace std;

inline int sgn(double x)
{
	if(x>-eps && x<eps) return 0;
	if(x>0) return 1;
	else 	return -1;
}
inline double sqr(double x)
{
	return x*x;
}

struct point
{
	double x,y;
	point(double a=0,double b=0)
	{
		x=a;y=b;
	}
	point operator + (const point &b)const
	{
		return point(x+b.x,y+b.y);
	}
	point operator - (const point &b)const
	{
		return point(x-b.x,y-b.y);
	}
	friend point operator * (const double t,const point &p)
	{
		return point(t*p.x,t*p.y);
	}
	inline double norm()
	{
		return sqrt(x*x+y*y);
	}
	inline void transxy(double b)//逆时针旋转b弧度
	{
		double tx=x,ty=y;
		x=tx*cos(b)-ty*sin(b);
		y=tx*sin(b)+ty*cos(b);
	}
	inline void transxy(double cosb,double sinb)
	{
		double tx=x,ty=y;
		x=tx*cosb-ty*sinb;
		y=tx*sinb+ty*cosb;
	}
};
inline double dot(const point &a,const point &b)
{
	return a.x*b.x+a.y*b.y;
}
inline double det(const point &a,const point &b)
{
	return a.x*b.y-a.y*b.x;
}
inline double dist(const point &a,const point &b)
{
	return (b-a).norm();
}
struct line
{
	point s,e;
	double k;
	line(point a=point(),point b=point())
	{
		s=a;e=b;
		k=atan2(e.y-s.y,e.x-s.x);
	}
};
inline bool point_on_seg(point &p,line &a)
{
	return sgn(det(p-a.s,p-a.e))==0 && sgn(dot(p-a.s,p-a.e))<=0;
}
inline double mysqrt(double x)
{
	return sqrt(max(x,0.0));
}
/*inline void circle_cross_line(line L,point o,double r,point ret[],int &num)
{
	point v=L.e-L.s;
	double t=dot(o-L.s,v)/dot(v,v);
	point rt=L.s+t*v;
	double dis=dist(rt,o);
	num=0; 
	if(sgn(dis-r)>0) 
		return;
	if(sgn(dis-r)==0)
	{
		if(point_on_seg(rt,L)) ret[num++]=rt;
		return;
	}
	double cosval=dis/r,sinval=mysqrt(1-cosval*cosval),sita;
	if(cosval<-1.0)
		cosval+=eps;
	if(cosval>1.0)
		cosval-=eps; 
	sita=acos(cosval);
	point p1=rt,p2=rt;
	//p1.transxy(cosval,sinval);p2.transxy(cosval,-sinval);
	p1.transxy(sita);p2.transxy(-sita);
	p1=(r/dis)*p1;p2=(r/dis)*p2;
	if(point_on_seg(p1,L)) 
		ret[num++]=p1;
	if(point_on_seg(p2,L))
		ret[num++]=p2;
}*/

inline void circle_cross_line(line L,point o,double r,point ret[],int &num)
{
	point a=L.s;point b=L.e;
	double x0=o.x,y0=o.y;
	double x1=a.x,y1=a.y;
	double x2=b.x,y2=b.y;
	double dx=x2-x1,dy=y2-y1;
	double A=dx*dx+dy*dy;
	double B=2*dx*(x1-x0)+2*dy*(y1-y0);
	double C=sqr(x1-x0)+sqr(y1-y0)-sqr(r);
	double delta=B*B-4*A*C;
	num=0;
 	if(sgn(delta)>=0)
    {
		double t1=(-B-mysqrt(delta))/(2*A);
		double t2=(-B+mysqrt(delta))/(2*A);
     	if(sgn(t1-1)<=0&&sgn(t1)>=0)
        	ret[num++]=point(x1+t1*dx,y1+t1*dy);
    	if(sgn(t2-1)<=0&&sgn(t2)>=0)
        	ret[num++]=point(x1+t2*dx,y1+t2*dy);
    }
}

double R,ans;
int n;
point a[maxl];

inline void prework()
{
	scanf("%d",&n);
	for(int i=0;i<n;i++)
		scanf("%lf%lf",&a[i].x,&a[i].y);
	a[n]=a[0];
}

double sector_area(const point &a,const point &b)
{
	double theta=atan2(a.y,a.x)-atan2(b.y,b.x);
	while(theta<=0) theta+=2*pi;
	while(theta>2*pi) theta-=2*pi;
	theta=min(theta,2*pi-theta);
	return R*R*theta/2;
}

inline double calc(const point &a,const point &b)
{
	point p[2];int num=0;
	bool ina=sgn(sqrt(dot(a,a))-R)<0,inb=sgn(sqrt(dot(b,b))-R)<0;
	if(ina)
	{
		if(inb) return fabs(det(a,b))/2;
		else
		{
			circle_cross_line(line(a,b),point(0,0),R,p,num);
            return fabs(sector_area(b,p[0]))+fabs(det(a,p[0]))/2.0;
		}
	}
	else
	{
		if(inb)
		{
			circle_cross_line(line(a,b),point(0,0),R,p,num);
			return sector_area(p[0],a)+fabs(det(p[0],b))/2;
		}
		else
		{
			circle_cross_line(line(a,b),point(0,0),R,p,num);
			if(num==2)
				return sector_area(a,p[0])+sector_area(p[1],b)+fabs(det(p[0],p[1]))/2.0;
			else
				return sector_area(a,b);
		}
	}
}

inline double area()
{
	double res=0;
	for(int i=0;i<n;i++)
	{
		int f=sgn(det(a[i],a[i+1]));
		if(f!=0)
			res+=f*(calc(a[i],a[i+1]));
	}
	return res;
}

inline void mainwork()
{
	ans=fabs(area())+eps;
}

inline void print()
{
	printf("%.2f\n",ans);
}

int main()
{
	while(~scanf("%lf",&R))
	{
		prework();
		mainwork();
		print();
	}	
	return 0;
}