Question 859243
Hint: Draw the picture to get



<img src="http://content.screencast.com/users/jim_thompson5910/folders/Snagit/media/cd5ef835-5101-4cf2-88f5-4b861037fae2/04.01.2014-16.45.png">



You are at point D. The length of CD is 16 feet. The center of the circle is point A. Point B is the point of tangency of line BD (angle ABD = 90 degrees) and segment BD = 25 feet.



The radius of the circle is unknown for now. We'll call it {{{r}}}



Now use the Pythagorean Theorem



{{{a^2 + b^2=c^2}}}



{{{r^2 + 25^2=(16+r)^2}}}



{{{r^2 + 625=256+32r+r^2}}}



{{{r^2 + 625-r^2=256+32r+r^2-r^2}}} Subtract {{{r^2}}} from both sides.



{{{625=256+32r}}}



I'll let you finish up.



Keep in mind that {{{d = 2r}}} where {{{d}}} is the diameter of the circle.