Let ABC be a triangle with ∠A=90o and ∠B<∠C. The tangent at A to the circumcircle k of △ABC intersects line BC at D. Let E be the reflection of A in BC. Also, let X be the feet of the perpendicular from A to BE and let Y be the midpoint of AX. Line BY meets k again at Z. Prove that line BD is tangent to the circumcircle of △ADZ. geometrytangentcircumcircleright triangle