chicha v1.3

import matplotlib.pyplot as plt
import matplotlib.patches
import matplotlib.path
import numpy as np
import math

class Line:
    def __init__(self, x1, y1, x2, y2):
        if x2<x1:
            self._x1=x2
            self._y1=y2
            self._x2=x1
            self._y2=y1
        else:
            self._x1=x1
            self._y1=y1
            self._x2=x2
            self._y2=y2
        self.xi=0
        self.yi=0
        self.xj=0
        self.yj=0

    def get_A(self):
        return self._y2-self._y1

    def get_B(self):
        return self._x1-self._x2

    def get_C(self):
        return self._x2*self._y1-self._x1*self._y2

    def info(self):
        print(self.get_A(), self.get_B(), self.get_C())

    def show(self):
        x=[self._x1,self._x2]
        y=[self._y1,self._y2]
        plt.plot(x, y)


    def angle(self):
        if self._x2-self._x1:
            return math.atan(abs(self._y2-self._y1)/abs(self._x2-self._x1))
        else:
            return math.pi/2

    def check_a(self):
        if self._x2-self._x1:
            return (self._y2-self._y1)/(self._x2-self._x1)
        else:
            return 1

    def check_ins(self, circle):
        if (self._x1<=circle.xi<=self._x2 and self._y1<=circle.yi<=self._y2 or self._x1<=circle.xj<=self._x2 and self._y1<=circle.yj<=self._y2) or self.check_a()<0 and (self._x1<=circle.xi<=self._x2 and self._y2<=circle.yi<=self._y1 or self._x1<=circle.xj<=self._x2 and self._y2<=circle.yj<=self._y1):
            return 1
        else:
            return 0

class Circle:
    def __init__(self, x=0., y=0., r=0.):
        self._x=x
        self._y=y
        self._r=r

    ##def input(self):
       ## self._x=float(input())
        ##self._y=float(input())
        ##self._r=float(input())

    def show(self):
        axes = plt.gca()
        axes.set_aspect("equal")
        cc = matplotlib.patches.Circle((self._x,self._y),self._r, fill=0)
        axes.add_patch(cc)

    def dist(self, line):
        a=line.get_A()
        b=line.get_B()
        c=line.get_C()
        return abs(a*self._x+b*self._y+c)/((a**2+b**2)**(1/2))

    def intersect(self, line):
        A=line.get_A()
        B=line.get_B()
        C=line.get_C()
        ys=(B*C+A*B*self._x-A**2*self._y)/(-A**2-B**2)
        if A:
            xs=-(B*ys+C)/A
        else:
            xs=self._x
        a=line.angle()
        l=(self._r**2-self.dist(line)**2)**(1/2)
        lx=l*math.cos(a)
        ly=l*math.sin(a)
        if line.check_a()>0:
            self.xi=xs-lx
            self.yi=ys-ly
            self.xj=xs+lx
            self.yj=ys+ly
        else:
            self.xi=xs-lx
            self.yi=ys+ly
            self.xj=xs+lx
            self.yj=ys-ly
        if line.check_a()>0 and line.check_ins(self):
            return 1
        else:
            return 0

    def check(self, line):
        if self.dist(line)>self._r or not self.intersect(line):
            return 0
        else:
            return 1

class Polygon:
    def __init__(self):
        self._P=[]
        self._L=[]

    def input(self, l):
        self._P=[[float(input()), float(input())] for i in range(l)]
        for i in range(l):
            if i+1<l:
                self._L.append(Line(self._P[i,0], self._P[i,1], self._P[i+1,0], self._P[i+1,1]))
            else:
                self._L.append(Line(self._P[i,0], self._P[i,1], self._P[0,0], self._P[0,1]))

    def check(self, circle):
        for i in self._L:
            if circle.check(i):
                return 1
        return 0

    def show(self):
        for i in self._L:
            i.show()
C=Circle(0., 0., 2)
P=Polygon()
##C.input()
n=int(input())
P.input(n)
print(P.check(C))
P.show()
C.show()
plt.show()