Circles w1 and w2 with centers at points O1 and O2 respectively, intersect at points A and B. A line passing through point B, intersects the circles w1 and w2 at points C and D other than B. Tangents to the circles w1 and w2 at points C and D intersect at point E. Line EA intersects the circumscribed circle w of triangle AO1O2 at point F. Prove that the length of the segment is EF is equal to the diameter of the circle w.(Vovchenko V., Plotnikov M.) geometrycircumcirclediametercircles