Question 431186
{{{drawing(225,200,-4,5,-4,4,
locate(-.3,1.8,r), locate(2,1.6,d),
circle(0,0,3), triangle(0,0,4,3,0,3),
locate(0,0,O), locate(4,3,P), locate(1.6,3.6,x),
rectangle(0,2.6,.4,3)



 )}}}
<pre>
A tangent to a circle makes a right angle with the
radius drawn to the point of tangency. So the triangle
drawn is a right triangle and the hypotenuse is d.

We want to find x.

Use the Pythagorean theorem:

r² + x² = d²

     x² = d² - r²
           _______ 
      x = &#8730;d² - r²  

Edwin</pre>