Let ABC be a right triangle with hypotenuse BC. The tangent to the circumcircle of triangle ABC at A intersects the line BC at T. The points D and E are chosen so that AD=BD,AE=CE, and ∠CBD=∠BCE<90∘. Prove that D,E, and T are collinear.Proposed by Nikola Velov, Macedonia geometrytangentcollinearJuniorBalkanshortlist