KöMaL 2020 B5101

$ABCDO$ is a four-sided pyramid, and $P$ is a point in the interior of base $ABCD$. A plane not passing through $O$ cuts the lines $OA$, $OB$, $OC$, $OD$ and $OP$ at points $A'$, $B'$, $C'$, $D'$, and $P'$, respectively. Prove that $\frac{t_{PAB}\cdot t_{PCD}}{t_{PBC}\cdot t_{PDA}} = \frac{t_{P'A'B'}\cdot t_{P'C'D'}}{t_{P'B'C'}\cdot t_{P'D'A'}},$ where $t_{XYZ}$ denotes the area of triangle $XYZ$.