$2009$ concentric circles are drawn with radii from $1$ unit to $2009$ units. From a point on the outermost circle, tangents are drawn to the inner circles. Discover the number of tangents which will have integer measure in the problem.
My approach to the problem is that since the tangents are perpendicular to the radius at the point of contact. This means that I could find all the Pythagorean triplets with $2009$ as one measure. However, I wasn't getting anywhere with that approach.