Maximum number of rings

There are a number of rings lying on the floor.
Any two rings can intersect at two points, may not intersect at all, or touch
each other at a single point. Two rings can be lifted simultaneously if and only
if they intersect at two points. A bunch of rings mutually satisfying this
condition can be lifted at once. You have to find the maximum number of rings
that can be lifted in a single attempt. The rings are specified by their x and y coordinates on the floor and their radius, the specifications of a ring being in a single row of a matrix.

        static void Main(string[]
args)

        {          

            int
maxcount = 1;

            double[,]
arr ={

                               {0.0, 0.0, 1.0},

                               {1.0, 0.0, 1.0},

                               {2.0, 0.0, 1.0},

                               {-1.0, 0.0, 1.0}

                           };

            int
num = arr.GetLength(0);

            //Array
to keep track of the rings included in the present bunch.

            int[]
used = new int[num];

            for
(int i = 0; i < arr.GetLength(0); i++)//Denotes the starting ring.

            {

                int
thiscount = 1;

                for
(int m = 0; m < num; m++)

                {

                    used[m] = 0;

                }

                used[i] = 1;//Starting ring has been used.

                //Searching
a ring from the beginning which matches the conditions.

                for
(int j = 0; j < arr.GetLength(0); j++)

                {                                               

                    if
(used[j] == 0)

                    {

                        //Searching from the beginning from the beginning of the current bunch.

                        for (int n = 0; n < num; n++)

                        {

                            double dist = Math.Sqrt(Math.Pow((arr[n, 0] - arr[j, 0]), 2.0d) + Math.Pow((arr[n, 1] - arr[j, 1]), 2.0d));

                            if (used[n] == 1 && dist < arr[j, 2] +
arr[n, 2] && dist > Math.Abs(arr[j,
2] - arr[n, 2]))

                            {

                                used[j] = 1;

                                thiscount++;

                                break;

                            }

                        }

                    }

                }

                if
(thiscount > maxcount)

                {

                    maxcount = thiscount;

                }

            }

            Console.WriteLine("The maximum number of rings is: " +
maxcount);

        }