Putnam 1949 A4

Given that $P$ is a point inside a tetrahedron with vertices at $A, B, C$ and $D$ , such that the sum of the distances $PA+PB+PC+PD$ is a minimum, show that the two angles $\angle APB$ and $\angle CPD$ are equal and are bisected by the same straight line. What other pair of angles must be equal?