Here we have right-angle triangle. Sides are:
AB = 19+x
BC= x
AC= 30
From the picture we can see that side AB is hypothenuze. We are given number 19 as part of length of that hypothenuze. Other part is equal to distance from center to edge of circle. This length is same as side BC.
We will use Pythagorean theorem to solve this:
[tex] (AB)^{2} = (BC)^{2} + (AC)^{2} \\ (19+x)^{2} = x^{2} + 30^{2} \\ 361+38x+ x^{2} = x^{2} +900 \\ x^{2} - x^{2} +38x=900-361 \\ 38x=539 \\ x=14.2yard[/tex]
