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

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