Distance from intersection of two lines to a circle

What is the distance from the intersection of two lines to a circle? Here's the graph of the problem with some appropriate notation. So I have to find the distance dW. But to make things more interesting, I want to know dW for several angles of the tangent to the circle (beta) and several positions of the vertical dotted red line (dE). I've tried trigonometry to solve this, but analytic geometry proved much simpler. So, the idea is simply to express the equation of the tangent line as:

 

so using the equation of the line:

The results are displayed in the next graph for all angles and positions of ther vertical line.