I wish to create 5 identical white circles of some lesser radius, which I will place on top of the black circle and completely obscure (cover) the black circle.

What is the smallest radius which I can make the smaller circles and still meet my requirement?

Gosh! So, what have I learned so far?

Okay. Charlie had the answer all along. Richard knew there was a simple constant and knew the history of the problem. Also he knows a bunch of secret website information. Cee? Well, nice try Cee. Nikki got the answer too, but made it a lot more clear. Well, to me anyway.

So, we merely needed to multiply the radius of the black circle by the reciprocal of phi to find the radius of the white circles we need to use. 5 times 0.618033988 = 3.09016994.

Wow! The Golden Ratio strikes again.