JMO 1997 Problem 4

Let $A,B,C,D$ be points in space which are not on a same plane and no any 3 points are not colinear. Suppose that the sum of the segments $AX+BX+CX+DX$ is minimized at $X=X_0$ which is different from $A,B,C,D.$ Prove that $\angle{AX_0B}=\angle{CX_0D}.$