(* The line going through the midpoints is parallel to the third side *)

Theorem th6_7 :
forall A B C L M N O : Point,
inter_ll L B C A O ->
inter_ll N B A C O ->
inter_ll M A C B O ->
S A M L * (S B N M * S C L N) = S A N L * (S B L M * S C N M).