MathNet 2004 — Part 02 Question 15

$ABCD$ is any quadrilateral, $P$ and $Q$ the midpoints of the diagonals $BD$ and $AC$, respectively. The parallels through $P$ and $Q$ to the other diagonal intersect at $O$. If we join $O$ with the four midpoints of the sides $X, Y, Z$ and $T$, four quadrilaterals $OXBY$, $OYCZ$, $OZDT$ and $OTAX$ are formed.

Prove that the four quadrilaterals have the same


area.