Hint Resolve para_not_eq_1 para_not_eq_2 para_not_eq_3
para_not_eq_4 para_not_eq_5 para_not_eq_6 : Geom.

Theorem mid_point_equation :
forall A C O P Q : Point,
Col O A C -> A <> C -> A ** O = O ** C ->
S A P Q + S C P Q = 2 * S O P Q.