Unstable Snowman
Q: Garabaggio's latest effort Unstable Snowman, currently on show at Rogues' Gallery on Poppycock Terrace consists of two circles that fit snugly into a square outline, Why even a fool could have done it!
If the radius of the small circle is r and the larger is R what is the side of the square?
For what values of R and r is the area of the square that they take up a maximum?
For what values a minimum?
SOURCE: Chris Maslanka's Pyrgic puzzle, The Guardian 28 September 2019.
A: k(R+r) where k = 1+1/sqrt(2); R = 1/2, r = (3-2sqrt(2))/2, assuming square has side 1; R = r = 1/(2k), with same assumption. Indeed, the area of the two circles lies between 53.9% and 80.9% the area of the square.