Require Export C9_Triangles_Emboites.
Section MIDPOINT.
Definition Middle (A B : Point) : Figure :=
fun I : Point => Collinear A B I /\ Distance I A = Distance I B.

Lemma UniqueMidPoint : forall (A B : Point) (H : A <> B) (C : Point),
Collinear A B C ->
Distance C A = Distance C B ->
C = MidPoint A B H.