线段是否和圆相交

#include<bits/stdc++.h>
using namespace std;
const double EPS = 1e-8;
struct point{
	double x, y;
};
point a, b, c; //线段ab， 圆心c
double r; // 半径r 
double mul(point p1, point p2, point p0){
    return (p1.x-p0.x)*(p2.y-p0.y)-(p2.x-p0.x)*(p1.y-p0.y);
}
double dist(point p1, point p2){
	return sqrt((p1.x-p2.x)*(p1.x-p2.x)+(p1.y-p2.y)*(p1.y-p2.y));
}
double p_to_line(point p, point L1, point L2){
	return fabs(mul(p, L1, L2)) / dist(L1, L2);
}
bool solve(point c, point L1, point L2){
	double t1 = dist(c, L1) - r, t2 = dist(c, L2) - r;
	point t = c;
	if(t1 < EPS || t2 < EPS) return t1 > -EPS || t2 > -EPS;
	t.x += L1.y - L2.y;
	t.y += L2.x - L1.x;
	return mul(L1, c, t) * mul(L2, c, t) < EPS && p_to_line(c, L1, L2) - r < EPS;	
}
int main()
{
	scanf("%lf %lf %lf %lf %lf %lf %lf", &a.x, &a.y, &b.x, &b.y, &c.x, &c.y, &r);
	if(solve(c, a, b)) cout << "相交" << endl;
	else cout << "不相交" << endl;
	return 0;	
}