The following is the 24th problem of the University of Waterloo’s Cayley Contest in 2022.
“A cube with edge length 8 is balanced on one of its vertices on a horizontal table such that the diagonal from this vertex through the interior of the cube to the farthest vertex is vertical. When the sun is directly above the top vertex, the shadow of the cube on the table is a regular hexagon. The area of this shadow can be written in the form 
, where 
and 
are positive integers and is not divisible by any perfect square larger than 1. What is the value of 
?”
I drew a cube using the Geogebra 3D Calculator. The cube can be rotated and panned-and-zoomed, which is helpful for understanding this problem.
https://www.geogebra.org/m/ca3dfseb
This post is also a test to embed LaTeX in WordPress. Thanks to QuickLaTeX.
Nice!