Given the equation of a circle and the points of contact of two tangents, is it possible to find their point of intersection?
The obvious method is to find the equation of the two tangents, using the fact that they are perpendicular to the radius and pass through the point of contact, and then find their point of intersection. However, this method gets a bit lengthy. I was wondering if there is an easier method to do this? Or maybe an easier method to derive the equation of the tangents at least?