Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

Cross Points of a Circe and a Line

For given a circle $c$ and a line $l$, print the coordinates of the cross points of them.

Input

The input is given in the following format.

$cx\; cy\; r$

$q$

$Line_1$

$Line_2$

:

$Line_q$

In the first line, the center coordinate of the circle and its radius are given by $cx$, $cy$ and $r$. In the second line, the number of queries $q$ is given.

In the following $q$ lines, as queries, $Line_i$ are given ($1 \leq i \leq q$) in the following format.

$x_1\; y_1\; x_2\; y_2$

Each line is represented by two points $p1$ and $p2$ which the line crosses. The coordinate of $p1$ and $p2$ are given by ($x1$, $y1$) and ($x2$, $y2$) respectively. All input values are given in integers.

Output

For each query, print the coordinates of the cross points in the following rules.

If there is one cross point, print two coordinates with the same values.

Print the coordinate with smaller $x$ first. In case of a tie, print the coordinate with smaller $y$ first.

The output values should be in a decimal fraction with an error less than 0.000001.

Constraints

$p1$ and $p2$ are different

The circle and line have at least one cross point

$1 \leq q \leq 1,000$

$-10,000 \leq cx, cy, x1, y1, x2, y2 \leq 10,000$

$1 \leq r \leq 10,000$

Sample Input and Output

Sample Input

2 1 1
2
0 1 4 1
3 0 3 3

Sample Output

1.00000000 1.00000000 3.00000000 1.00000000
3.00000000 1.00000000 3.00000000 1.00000000

Solution in C# (judge verdict: Accepted)

using System;
using System.IO;
using System.Linq;
using System.Text;
using System.Collections.Generic;
using System.Diagnostics;
//using System.Numerics;
using Enu = System.Linq.Enumerable;

public class Program
{
    public void Solve()
    {
        var P = new Point(Reader.Double(), Reader.Double());
        double R = Reader.Double();
        int NQ = Reader.Int();


        for (int q = 0; q < NQ; q++)
        {
            var A = new Point(Reader.Double(), Reader.Double());
            var B = new Point(Reader.Double(), Reader.Double());
            var line = new Line(A, B);
            var cross = Intersection(P, R, line);
            if (cross.Length == 1) Console.WriteLine(cross[0] + " " + cross[0]);
            else Console.WriteLine(cross[0] + " " + cross[1]);
        }

        Console.ReadLine();
    }

    public Point[] Intersection(Point circleCenter, double r, Line line)
    {
        const double EPS = 1e-10;
        var v = line.B - line.A;
        var p = line.A + v * (v.Dot(circleCenter - line.A) / v.Dot(v));
        double d = p.Distance(circleCenter);
        if (d > r) return new Point[0];
        if (Math.Abs(d - r) < EPS) return new Point[1] { p };
        var e = (line.B - line.A) * (1.0 / (line.B - line.A).Norm);
        var m = Math.Sqrt(r * r - (p - circleCenter).Dot(p - circleCenter));
        var A = p - e * m;
        var B = p + e * m;
        if (A.CompareTo(B) <= 0) return new Point[] { A, B };
        return new Point[] { B, A };
    }

    public class Line
    {
        public Point A, B;
        public Point this[int i]
        {
            get { if (i == 0) return A; if (i == 1) return B; throw new ArgumentException(); }
        }
        public Line(Point a, Point b) { Debug.Assert(a != b); A = a; B = b; }
        public override string ToString() { return A + " - " + B; }
    }

    public struct Point : IEquatable<Point>, IComparable<Point>
    {
        public static readonly double Eps = 1e-10;
        public double X, Y;
        public string Label;

        public Point(double x, double y) { X = x; Y = y; Label = ""; }
        public Point(double x, double y, string s) { X = x; Y = y; Label = s; }

        public static Point operator +(Point a, Point b)
        {
            return new Point(Add(a.X, b.X), Add(a.Y, b.Y));
        }
        public static Point operator -(Point a, Point b)
        {
            return new Point(Add(a.X, -b.X), Add(a.Y, -b.Y));
        }
        public static Point operator *(double d, Point p)
        {
            return new Point(p.X * d, p.Y * d);
        }
        public static Point operator *(Point p, double d) { return d * p; }
        public double Norm { get { return Math.Sqrt(Add(X * X, Y * Y)); } }
        public double Distance(Point b) { return (b - this).Norm; }
        public double Dot(Point b) { return Add(X * b.X, Y * b.Y); }
        public double Det(Point b) { return Add(X * b.Y, -Y * b.X); }
        public bool Equals(Point b) { return X == b.X && Y == b.Y; }
        public override bool Equals(object obj) { return Equals((Point)obj); }
        public static bool operator ==(Point a, Point b) { return a.Equals(b); }
        public static bool operator !=(Point a, Point b) { return !a.Equals(b); }
        public int CompareTo(Point b) { return X != b.X ? Math.Sign(X - b.X) : Math.Sign(Y - b.Y); }
        public override int GetHashCode() { return (int)(X * 100000 + Y); }
        public override string ToString() { return X + " " + Y; }

        private static double Add(double a, double b)
        {
            if (Math.Abs(a + b) < Eps * (Math.Abs(a) + Math.Abs(b))) return 0;
            return a + b;
        }
    }
}


class Entry { static void Main() { new Program().Solve(); } }
class Reader
{
    private static TextReader reader = Console.In;
    private static readonly char[] separator = { ' ' };
    private static readonly StringSplitOptions op = StringSplitOptions.RemoveEmptyEntries;
    private static string[] A = new string[0];
    private static int i;
    private static void Init() { A = new string[0]; }
    public static void Set(TextReader r) { reader = r; Init(); }
    public static void Set(string file) { reader = new StreamReader(file); Init(); }
    public static bool HasNext() { return CheckNext(); }
    public static string String() { return Next(); }
    public static int Int() { return int.Parse(Next()); }
    public static long Long() { return long.Parse(Next()); }
    public static double Double() { return double.Parse(Next()); }
    public static int[] IntLine() { return Array.ConvertAll(Split(Line()), int.Parse); }
    public static int[] IntArray(int N) { return Enu.Range(0, N).Select(i => Int()).ToArray(); }
    public static int[][] IntTable(int H) { return Enu.Range(0, H).Select(i => IntLine()).ToArray(); }
    public static string[] StringArray(int N) { return Enu.Range(0, N).Select(i => Next()).ToArray(); }
    public static string Line() { return reader.ReadLine().Trim(); }
    private static string[] Split(string s) { return s.Split(separator, op); }
    private static string Next() { CheckNext(); return A[i++]; }
    private static bool CheckNext()
    {
        if (i < A.Length) return true;
        string line = reader.ReadLine();
        if (line == null) return false;
        if (line == "") return CheckNext();
        A = Split(line);
        i = 0;
        return true;
    }
}