Setting up some equations

Let x and y represent the distances as labelled on the figure. 

Then similar triangles gives

Also, the Pythagorean relationship gives

So we have a system of two equations in two variables and we can graph them on the same axes. The first is a rectangular hyperbola and the second is a circle.

Only the first quadrant is of interest. Why?

 

 

Now, solve:
 

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