Let ABC be an acute triangle such that AH=HD, where H is the orthocenter of ABC and D∈BC is the foot of the altitude from the vertex A. Let ℓ denote the line through H which is tangent to the circumcircle of the triangle BHC. Let S and T be the intersection points of ℓ with AB and AC, respectively. Denote the midpoints of BH and CH by M and N, respectively. Prove that the lines SM and TN are parallel. geometrymidpointsparallelorthocenteraltitudeJBMOJunior Balkan