Proof with Geometry.
intros...
assert (P ** A / O ** A = S P B A / S O B A)...
assert (S P A B = - S P B A)...
assert (S O A B = - S O B A)...
rewrite H3...
rewrite H4...
rewrite H2...
assert (S O B A <> 0)...
field...
Qed.
Hint Resolve A6_5: Geom.

Theorem A6_6 :
forall A B R Q : Point,
A <> Q -> ~ Col Q A B -> Col A R Q -> A ** R / A ** Q = S R A B / S Q A B.