题解 | 【模板】点圆位置关系

#include <bits/stdc++.h>
using ll = long long;
using namespace std;
ll oljl(ll x1, ll y1, ll x2, ll y2) {
    return (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
}
int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    cout << fixed << setprecision(12);
    ll t;
    cin >> t;
    while (t--) {
        ll xo, yo, r, xa, ya;
        cin >> xo >> yo >> r >> xa >> ya;       
        ll res = oljl(xo, yo, xa, ya);
        ll jl = r * r;       
        if (res == jl) {
            cout << '2' << endl;
            continue;
        } else if (res < jl) {
            cout << '1' << endl;
            continue;
        } else {
            double dx = xa - xo;
            double dy = ya - yo;
            double d2 = res; 
            double sqrt_val = sqrt(d2 - jl);
            // 第一个切点的横坐标
            double x1 = xo + (jl * dx - r * dy * sqrt_val) / d2;
            // 第二个切点的横坐标
            double x2 = xo + (jl * dx + r * dy * sqrt_val) / d2;
            // 对应的纵坐标
            double y1 = yo + (jl * dy + r * dx * sqrt_val) / d2;
            double y2 = yo + (jl * dy - r * dx * sqrt_val) / d2;
            cout << "3 " << x1 << " " << y1 << " " << x2 << " " << y2 << endl;
        }
    }
    return 0;
}