投稿日 11/4/2019最終更新日 11/4/2019

# 問題

http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_D

# 解説

円と直線の交点を求めるアルゴリズムについては以下リンクを参照.

# 解答

C++

// C++ 14
#include <iostream>
#include <string>
#include <vector>
#include <list>
#include <algorithm>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <unordered_map>
#include <math.h>

#define ll long long
#define Int int
#define loop(x, start, end) for(Int x = start; x < end; x++)
#define loopdown(x, start, end) for(int x = start; x > end; x--)
#define rep(n) for(int x = 0; x < n; x++)
#define span(a,x,y) a.begin()+x,a.begin()+y
#define span_all(a) a.begin(),a.end()
#define len(x) (x.size())
#define last(x) (*(x.end()-1))

using namespace std;

#define EPS 0.0000000001
#define fequals(a,b) (fabs((a) - (b)) < EPS)

class Vector2 {
public:
  double x, y;
  
  Vector2(double x = 0, double y = 0): x(x), y(y) {}
  
  Vector2 operator + (const Vector2 v) const { return Vector2(x + v.x, y + v.y); }
  Vector2 operator - (const Vector2 v) const { return Vector2(x - v.x, y - v.y); }
  Vector2 operator * (const double k) const { return Vector2(x * k, y * k); }
  Vector2 operator / (const double k) const { return Vector2(x / k, y / k); }
  
  double length() { return sqrt(norm()); }
  double norm() { return x * x + y * y; }
  double dot (Vector2 const v) { return x * v.x + y * v.y; }
  double cross (Vector2 const v) { return x * v.y - y * v.x; }
  
  bool parallel(Vector2 &other) {
    return fequals(0, cross(other));
  }
  
  bool orthogonal(Vector2 &other) {
    return fequals(0, dot(other));
  }
  
  bool operator < (const Vector2 &v) {
    return x != v.x ? x < v.x : y < v.y;
  }
  
  bool operator == (const Vector2 &v) {
    return fabs(x - v.x) < EPS && fabs(y - v.y) < EPS;
  }
};

ostream & operator << (ostream & out, Vector2 const & v) { 
  out<< "Vector2(" << v.x << ", " << v.y << ')';
  return out;
}

istream & operator >> (istream & in, Vector2 & v) { 
  double x, y;
  in >> x;
  in >> y;
  v.x = x;
  v.y = y;
  return in;
}

Int N;
double R;
Vector2 C, p1, p2;


Vector2 project(Vector2 start_, Vector2 end_, Vector2 p) {
    Vector2 v = end_ - start_;
    return start_ + v * (v.dot(p - start_) / v.norm());
}

Vector2 unitVec(Vector2 v) {
  return v / v.length();
}

pair<Vector2, Vector2> crossPoints() {
  Vector2 p = project(p1, p2, C);
  Vector2 e = unitVec(p2 - p1);
  double len = sqrt(R*R - (p - C).norm());
  Vector2 x1 = p + e * len;
  Vector2 x2 = p + e * (-len);
  if (fabs(x1.x) < EPS) x1.x = 0.0;
  if (fabs(x1.y) < EPS) x1.y = 0.0;
  if (fabs(x2.x) < EPS) x2.x = 0.0;
  if (fabs(x2.y) < EPS) x2.y = 0.0;
  if (x1 < x2) return make_pair(x1, x2);
  return make_pair(x2, x1);
}

void solve() {
  auto points = crossPoints();
  cout << points.first.x << ' ' << points.first.y << ' ';
  cout << points.second.x << ' ' << points.second.y << endl;
}

void input() {
  cin >> C >> R >> N;
  while (cin >> p1 >> p2) {
    solve();
  }
}

int main() {
  cout.precision(15);
  input();
}