Question 177
Regular tetrahedron $A B C D$ is projected onto a plane sending $A, B, C$, and $D$ to $A', B', C'$, and $D'$ respectively. Suppose $A' B' C' D'$ is a convex quadrilateral with $A' B' = A' D'$ and $C' B' = C' D'$, and suppose that the area of $A' B' C' D' = 4$. Given these conditions, the set of possible lengths of $A B$ consists of all real numbers in the interval $[a, b)$. Compute $b$.