Problem 2

Part of 1981 Yugoslav Team Selection Test

Problems(1)

point divides quadrilateral into four equal triangles

Source: Yugoslav TST 1981 P2

Suppose that there is a point

S

inside a quadrilateral

ABCD

such that segments

SA,SB,SC,SD

divide the quadrilateral into four triangles of equal areas. Prove that one of the diagonals of the quadrilateral bisects the other one.