Squeezing Mickey
Geometry
Level
4
Three unit circles are squeezed into the smallest sized square possible.
What is the side length of the square to 3 decimal places?
Image credit: https://commons.wikimedia.org
The answer is 3.932.
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1 solution
From the picture, by symmetry, we will only have a square if the segments connecting the midpoints (forming an equilateral triangle) make an angle of 15 degrees with respect to the sides of the square as shown:
So, we can see that the side length, L , will be given by:
L = 2 + 2 cos 1 5 o = 3 . 9 3 2