题解 | 直线与圆交点间距

#include <bits/stdc++.h>
using namespace std;

struct point {
    double x, y;
    point(double A, double B) {
        x = A, y = B;
    }
    point() = default;
};

struct line {
    point point_A, point_B;
    line(point A, point B) {
        point_A = A, point_B = B;
    }
    line() = default;
};

struct Circle {
    point O;
    int r;
    Circle(point A, int B) {
        O = A, r = B;
    }
    Circle() = default;
};

double getDistance(const Circle& circle, const line& l) {
    // 请在这里实现你的代码
    double ox = circle.O.x, oy = circle.O.y;
    double r = circle.r;
    double x1 = l.point_A.x, y1 = l.point_A.y;
    double x2 = l.point_B.x, y2 = l.point_B.y;

    // 计算直线方程的参数 A, B, C
    double A = y2 - y1;
    double B = x1 - x2;
    double C = x2 * y1 - x1 * y2;

    // 计算圆心到直线的距离 d
    double d = abs(A * ox + B * oy + C) / sqrt(A * A + B * B);

    // 计算两点间的距离
    if (d < r) {
        return 2 * sqrt(r * r - d * d);
    } else if (d == r) {
        return 0.0;
    }
    // 根据题目备注，直线与圆不相离，所以不需要处理 d > r 的情况
    return 0.0;
}

int main() {
    double ox, oy, r;
    double x1, y1, x2, y2;

    cin >> ox >> oy >> r;
    cin >> x1 >> y1 >> x2 >> y2;

    point center(ox, oy);
    Circle circle(center, (int)r);

    point p1(x1, y1);
    point p2(x2, y2);
    line l(p1, p2);

    double result = getDistance(circle, l);
    cout << fixed << setprecision(6) << result << endl;

    return 0;
}