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)
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