Since we know that the 38 is being bisected (which we can tell by the fact that the line hits it perpendicularly), we know that from the intersection to the edge of the circle is 19. From this we can create a right triangle in which the legs are 10 and 19 and the hypotenuse is a radius of the circle. Since x is also a radius of the circle, all we have to do is use that information to find the hypotenuse using the Pythagorean Theorem and we have x.
Pythagorean Theorem
+ 
= 
+ 
= 
100 + 361 =
461 =
x =
or about 21.47
Pythagorean Theorem
100 + 361 =
461 =
x =