This circle centre finder will make it super easy when you next need to find the centre of a circle. 

Just put the circle so that it meets both edges of the right angle and so that the 45 degree section is passing through the middle of the circle. Then just score a line and rotate your circle 90 degrees and repeat. The point where the lines intersect is the middle of the wood. 

This jig can be used on circles up to a diameter of about 450mm, or just under 18 inches. You could easily use it on larger pieces by just scaling the size of the model up. Another option is to scale it down so that it can be used on dowels.