r = 11 in.
central angle is 360/10 = 36°
drawing a rough sketch, the median to the line between the holes,from the center if the circle, is a perpendicular bisector of that line.
Then:
sin(18°) = (X/2)/11
11 x sin(18°) = x/2
X = 22 x sin(18°) = 6.8 in
