RO-TST 1992 Problem 10

In a tetrahedron $VABC$ , let $I$ be the incenter and $A',B',C'$ be arbitrary points on the edges $AV,BV,CV$ , and let $S_a,S_b,S_c,S_v$ be the areas of triangles $VBC,VAC,VAB,ABC$ , respectively. Show that points $A',B',C',I$ are coplanar if and only if $\frac{AA'}{A'V}S_a +\frac{BB'}{B'V}S_b +\frac{CC'}{C'V}S_c = S_v$