KöMaL 2024 B5429

For every points $X$, $Y$, $Z$, denote by $[XYZ]$ the area of triangle $XYZ$. Show that if points $A$, $B$, $C$, $D$, $E$, $F$ lie on a non-degenerate conic section then ${[ABC]\cdot[CDE]\cdot[EFA]\cdot[BDF]=[BCD]\cdot[DEF]\cdot[FAB]\cdot[ACE]}$.