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

Theorem th6_6 :
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 ->
A <> L ->
B <> M ->
C <> N ->
parallel O L A L ->
parallel O M B M ->
parallel O N C N -> O ** L / A ** L + O ** M / B ** M + O ** N / C ** N = 1.