End PerpBisect_2.
Hint Resolve perp_bisect_cong_1 perp_bisect_cong_2 : cong.
Section PerpBisect_3.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

Lemma perp_bisect_cong :
forall A A1 B B1 C C1 O: Tpoint,
~ Col A B C ->
Perp_bisect O A1 B C -> Perp_bisect O B1 A C -> Perp_bisect O C1 A B ->
Cong A O B O -> Cong B O C O ->
Cong A O C O.