(* elimination of ratios for euclidean constructions *)
(* the condition A<>Y is required *)

Theorem elim_ratio_on_perp_d_a :
forall Y P Q A C D : Point, forall r: F,
on_perp_d Y P Q r->
Col A P Y  ->
parallel A Y C D ->
C<>D ->
A<>Y ->
A**Y / C**D = (S A P Q -r/(2+2) * Py P Q P)/(S4 C P D Q).