Problem:
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Tangent to a Circle

Find the tangent lines between a point $p$ and a circle $c$.

Input

The input is given in the following format.

$px \; py$

$cx \; cy \; r$

$px$ and $py$ represents the coordinate of the point $p$. $cx$, $cy$ and $r$ represents the center coordinate and radius of the circle $c$ respectively. All input values are given in integers.

Output

Print coordinates of the tangent points on the circle $c$ based on the following rules.

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 0.00001.

Constraints

$-1,000 \leq px, py, cx, cy \leq 1,000$

$1 \leq r \leq 1,000$

Distance between $p$ and the center of $c$ is greater than the radius of $c$.

Sample Input 1

0 0
2 2 2

Sample Output 1

0.0000000000 2.0000000000
2.0000000000 0.0000000000

Sample Input 2

-3 0
2 2 2

Sample Output 2

0.6206896552 3.4482758621
2.0000000000 0.0000000000

Solution in C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace ConsoleApplication1
{
    enum ST { Bottom, Left, Right, Top }

    class Program
    {
        static void Main(string[] args)
        {
            double[] input = Array.ConvertAll(Console.ReadLine().Split(' '), double.Parse);
            Point p = new Point(input[0], input[1]);

            input = Array.ConvertAll(Console.ReadLine().Split(' '), double.Parse);
            Circle c = new Circle(new Point(input[0], input[1]), input[2]);

            var points = Contact(c, p);

            StringBuilder sb = new StringBuilder();
            foreach (var point in points) sb.AppendLine(point.ToString());
            Console.Write(sb);
        }

        static Point[] Contact(Circle c, Point p)
        {
            Point cp = p - c.p;
            double d = Math.Sqrt(cp.Norm - c.r * c.r);
            double k = c.r / cp.Norm;
            double r = c.r * k;
            double ds = d * k;

            double ax = c.p.x + cp.x * r - cp.y * ds;
            double ay = c.p.y + cp.y * r + cp.x * ds;
            double bx = c.p.x + cp.x * r + cp.y * ds;
            double by = c.p.y + cp.y * r - cp.x * ds;

            Point[] ret = new Point[] { new Point(ax, ay), new Point(bx, by) };
            Array.Sort(ret);
            return ret;
        }
    }

    class EndPoint : IComparable
    {
        internal Point p;
        internal int seg;
        internal ST st;

        public EndPoint(Point p, int seg, ST st)
        {
            this.p = p;
            this.seg = seg;
            this.st = st;
        }

        public int CompareTo(object obj)
        {
            EndPoint other = obj as EndPoint;

            if (p.y < other.p.y) return -1;
            if (p.y > other.p.y) return 1;
            if (st < other.st) return -1;
            if (st > other.st) return 1;
            return 0;
        }
    }

    class Point : IComparable
    {
        static readonly double EPS = 1E-10;

        internal double x, y;

        public Point(double x, double y)
        {
            this.x = x;
            this.y = y;
        }

        public double Abs { get { return Math.Sqrt(Norm); } }
        public double Norm { get { return x * x + y * y; } }

        public double Dot(Point p) { return x * p.x + y * p.y; }
        public double Cross(Point p) { return x * p.y - y * p.x; }
        public double Distance(Point p) { return (this - p).Abs; }

        public static Point operator +(Point a, Point b) { return new Point(a.x + b.x, a.y + b.y); }
        public static Point operator -(Point a, Point b) { return new Point(a.x - b.x, a.y - b.y); }
        public static Point operator *(Point p, double d) { return new Point(p.x * d, p.y * d); }
        public static Point operator /(Point p, double d) { return new Point(p.x / d, p.y / d); }
        public static bool operator <(Point a, Point b) { return Math.Abs(a.x - b.x) > EPS ? a.x < b.x : a.y < b.y; }
        public static bool operator >(Point a, Point b) { return Math.Abs(a.x - b.x) > EPS ? a.x > b.x : a.y > b.y; }
        public static bool operator ==(Point a, Point b) { return Math.Abs(a.x - b.x) < EPS && Math.Abs(a.y - b.y) < EPS; }
        public static bool operator !=(Point a, Point b) { return Math.Abs(a.x - b.x) >= EPS || Math.Abs(a.y - b.y) >= EPS; }

        public int CompareTo(object obj)
        {
            var other = obj as Point;
            if (obj == null) return -1;

            ComparerX compX = new ComparerX();
            return compX.Compare(this, other);
        }

        public override bool Equals(object obj)
        {
            var other = obj as Point;
            return Math.Abs(x - other.x) < EPS && Math.Abs(y - other.y) < EPS;
        }

        public override int GetHashCode()
        {
            return x.GetHashCode() ^ y.GetHashCode();
        }

        public override string ToString()
        {
            return string.Format("{0:f10} {1:f10}", x, y);
        }
    }

    class ComparerX : IComparer<Point>
    {
        static readonly double EPS = 1E-10;

        public int Compare(Point a, Point b)
        {
            if (a.x - b.x < -EPS) return -1;
            if (a.x - b.x > EPS) return 1;
            if (a.y - b.y < -EPS) return -1;
            if (a.y - b.y > EPS) return 1;
            return 0;
        }
    }

    class ComparerY : IComparer<Point>
    {
        static readonly double EPS = 1E-10;

        public int Compare(Point a, Point b)
        {
            if (a.y - b.y < -EPS) return -1;
            if (a.y - b.y > EPS) return 1;
            if (a.x - b.x < -EPS) return -1;
            if (a.x - b.x > EPS) return 1;
            return 0;
        }
    }

    class Segment
    {
        internal Point p1, p2;

        public Segment(Point p1, Point p2)
        {
            this.p1 = p1;
            this.p2 = p2;
        }
    }

    class Circle
    {
        internal Point p;
        internal double r;

        public Circle(Point p, double r)
        {
            this.p = p;
            this.r = r;
        }
    }
}