Question 613306
Draw out a picture to get


<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/05-21-2012-2.png">


Note: the diameter is 26, so the radius is 26/2 = 13. Also, the chord is bisected by the diameter, which allows us to cut that chord of 10 in half to get 2 pieces of 5.



So we can see we have a right triangle. Let's use the pythagorean theorem to solve for x


a^2+b^2 = c^2


5^2+x^2 = 13^2


25+x^2 = 169


x^2 = 169-25


x^2 = 144


x = sqrt(144)


x = 12


So the distance from the center to the chord is <font color="red">12 feet</font>.