Note that you can find OC where C is the center of a chord. It does not depend on the position of the chord.
I guess what you are saying is this: the problem was to prove that the midpoints of chords form a circle. Yes; this circle with radius OC is not shown in the picture. The circle that is shown is the original one with radius 8cm.
Because the distance OC from the center of the circle to the midpoint is always the same for each chord. Conversely, for each point C at this distance from O there is a chord of length 4cm of which C is the center.Why is it the case too that the midpoints create a circle..it's still not so clear..