public static double[] GetTangentPoints(

    double px,

    double py,

    double cx,

    double cy,

    double radius)

{

    var points = new double[4];

​

    var dx = cx - px;

    var dy = cy - py;

    if (dx == 0 && dy == 0)

        return null; // no solution

​

    // PC is distance between P and C, pc2 is PC^2

    var pc2 = dx * dx + dy * dy;

    var pc = Math.Sqrt(pc2);

    if (pc < radius)

        return null; // no solution

​

    // R is radius of  circle centered in P, r2 is R^2

    var r2 = pc2 - radius * radius;

​

    // d is the P => X0 distance (demonstration is here https://mathworld.wolfram.com/Circle-CircleIntersection.html where PC is named 'd' in there)

    var d = r2 / pc;

​

    // h is the X0 => X1 (and X0 => X2) distance

    var h = Math.Sqrt(r2 - d * d);

​

    // first tangent point

    points[0] = px + (dx * d - dy * h) / pc;

    points[1] = py + (dy * d + dx * h) / pc;

​

    // second tangent point

    points[2] = px + (dx * d + dy * h) / pc;

    points[3] = py + (dy * d - dx * h) / pc;

​

    return points;

}