Nice geometry lesson. For a 12 section plate I'd draw it out with a compass and ruler.
Start with a center point. Set your compass to the radius of your inner circle and draw your inner circle.
Without changing your radius put the point of your compass on the circle you just drew.
Mark from that point to the next on the circle. It will take 6 marks to go completely around the circle.
Draw a line from the center of your circle thru one of the marks you just made out past where your outer circle will be.
Now set your compass to the radius of your outer circle and draw your outer circle using the same center point as the first.
Start where the line you drew from the center crosses your outer circle and mark around your outer circle just like you did with the first one. You now have your inner and outer circles with 6 evenly spaced sections.
To get 12 petals put your compass point on one of the marks on the outer circle and make a short arc outside the circle. Move your compass to the next section and cross the first arc with another arc.
Draw a line from the center of the circle thru where those two arcs cross.
Now move your compass to where your line crosses the outer circle and mark around your outer circle again 6 times. Draw lines from the center of your circles thru each of those marks and you will end up with 12 evenly sized sections for your plate. From there it's a simple matter to add seam allowances to one of the sections for your template.
Easier to do than to type out or read about.
Clear as mud?
Rodney