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_is_on_perp_bisect :
forall A B C P,
Is_on_perp_bisect P A B ->
Is_on_perp_bisect P B C ->
Is_on_perp_bisect P A C.