Step 1: Let's do some figurin'
How to draw an octagon (pic 2)
Taking your width measurement+1/2" and draw a square with each side equal to that length.
Draw an "X" by connecting the corners diagonally with a line.
Place your compass point on a corner of the square and draw an arc 1/2 the length of the diagonal (from corner to center of square). Repeat for each corner.
Simply connect the ends of the arcs and you have an octagon.
To be an octagon, all eight sides should be equal when you're done. The drawing you made is an optical illusion as the angled lines appear shorter, but in fact they are all equal. Measure one of the sides. This is the length of your 8 pieces along the inside edge of your ring. In pic 3 you can see the side pieces are actually longer than this measurement because of their angled ends. Just remember to draw your cut line on the edge that will be inside the octagon. If you mark your cuts on the outside edge or face of the wood, your octagon will be too small.