(** * Proposition 11 If two circles touch one another internally, and their centers are taken, the straight line joining their centers, being produced, will fall on the point of contact of the circles. *)
(** * Proposition 12 If two circles touch one another externally, the straight line joining their centers will pass through the point of contact. *)
(** In our formalization we do not need to distinguish between the two kinds of tangency. *)

Lemma prop_11_12 : forall A B C D X,
TangentCC A B C D ->
OnCircle X A B ->
OnCircle X C D ->
Col X A C.