Radius and Diameter - the Relationship

"They learn what to observe, and make discoveries for themselves, original so far as they are concerned." ~ Charlotte Mason Vol 3 pg 238

Of all subjects I have found mathematics to be the most difficult to apply Miss Mason's principles to. Last week the concepts of radius and diameter were introduced to Georgi in our math text Life of Fred - Fractions.
I thought she grasped the concept pretty well, but today, she was at a total loss as to how to figure out the diameter of a circle whose radius was 32.
After numerous attempts to prod her memory I finally thought about Miss Mason's emphasis on children discovering ideas for themselves, owning the information. I thought, "What's the CM way to teach this" then I used a compass to draw several circles on a piece of paper, told her to draw a line and measure the radius, then the diameter and figure out what the relationship is between them.

After four circles she told me the radius is half the diameter and the diameter is two times the radius. Yes! Now the really neat part is that late this evening, eight hours after she made this discovery, out of the blue, I asked her to tell me the relationship between the radius and diameter of a circle. She didn't hesitate as she rattled off the answer. She discovered it. She remembers it. It is hers.