Triangle ΔABC is inscribed in circle Ω. The tangency point of Ω and the A-mixtilinear circle of ΔABC is T. Points E, F were chosen on AC, AB respectively so that EF∥BC and (TEF) is tangent to Ω. Let ω denote the A-excircle of ΔAEF, which is tangent to sides EF, AE, AF at K, Y, Z respectively. Line AT intersects ω at two points P, Q with P between A and Q. Let QK and YZ intersect at V, and let the tangent to ω at P and the tangent to Ω at T intersect at U. Prove that UV∥BC. olympic revengegeometrymixtilinear