An extension to Miquel theorem ?

On the sides (and continuations) of triangle ABC take points Ac, Bc, ..., Ab :

on AB : Ac, Bc, s.t. A→Ac = B→Bc;

on BC : Ba, Ca, s.t. B→Ba = C→Ca;

on CA : Cb, Ab, s.t. C→Cb = A→Ab;

(A→Ac is the vector from A to Ac)

Let tA, tB, tC be the tangents to the circumcircles of AAbAc, BBaBc, CCbCa at A, B, C.

Then tA, tB, tC are concurrent or all parallel.

(Drag red points)