Circle, tangent line, and a point not on the circle

http://www.webassign.net/userimages/...gentlines1.jpg

Suppose you have a unit circle and a point P with coordinates (4, 2). The task is to find the tangent points.

Here are my steps:

1. Name the coordinates of the tangent point in quadrant II as (r, s).

2. The slope of the tangent line is m = (s/r)

3. Rewrite the tangent point as (r, sqrt(1-r^2))

This is as far as I get before everything breaks down. Am I right so far?

4. My next step is to try to solve for r by using y = mx + b and the two points. But I end up with an ugly equation involving rational terms, radial terms, etc. and always end up with the wrong answer even when I cheat with a graphing calculator. Any idea what I'm doing wrong?