Calculates the intersection of a vector (given by two points) with a circle (point and radius)

CalculateVectorCircleIntersection.cs

using System;
using System.Drawing;

namespace ConsoleApplication1
{
    internal class Program
    {
        private static void Main()
        {
            Point start = new Point(0, 0);
            Point end = new Point(100, 12);

            Point circle = new Point(50, 0);
            double radius = 10;




            double a = Math.Pow(end.X - start.X, 2) + Math.Pow(end.Y - start.Y, 2);

            double b = 2 * (end.X - start.X) * (start.X - circle.X) + 2 * (end.Y - start.Y) * (start.Y - circle.Y);

            double c = Math.Pow(start.X - circle.X, 2) + Math.Pow(start.Y - circle.Y, 2) - Math.Pow(radius, 2);

            double t = (2 * c) / (-b + Math.Sqrt(Math.Pow(b, 2) - 4 * a * c));

            Console.WriteLine($"root: {t}");

            int tx = (int)Math.Round((end.X - start.X) * t + start.X);

            int ty = (int)Math.Round((end.Y - start.Y) * t + start.Y);

            Console.WriteLine($"intersection: {tx},{ty}");

            Console.ReadLine();
        }
    }
}