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

Theorem th6_42 :
forall A B C L M N P K : Point,
is_midpoint M A B ->
is_midpoint N A C ->
is_midpoint K B C ->
is_midpoint L A K ->
on_inter_parallel_parallel P A C M K B N ->
P<>A ->
(2 + 2) * S A K P = (1 + 2) * S A B C.