Circles ω1 and ω2 intersect at points A and B. At point A to ω1 and ω2 the tangents ℓ1 and ℓ2 are drawn respectively. The points T1 and T2 are chosen respectively on the circles ω1 and ω2 so that the angular measures of the arcs T1A and AT2 are equal (the measure of the circular arc is calculated clockwise). The tangent t1 at the point T1 to the circle ω1 intersects ℓ2 at the point M1. Similarly, the tangent t2 at the point T2 to the circle ω2 intersects ℓ1 at point M2. Prove that the midpoints of the segments M1M2 are on the same a straight line that does not depend on the position of points T1, T2. geometrycollinearLocuscircles