Question 29
We are given a tetrahedron with 5 edges of length $2$ and one of length $1$. A point $P$ either in the interior of the tetrahedron or on its surface (but not outside the tetrahedron) has distances from the surfaces of the tetrahedron we name $a, b, c$ and $d$. For which points $P$ is the value of $a+b+c+d$ minimal and for which is maximal?