Let AD be an altitude of triangle ABC, and let M, N and P be midpoints of AB, AD and BC, respectively. Furthermore let K be a foot of perpendicular from point D to line AC, and let T be point on extension of line KD (over point D) such that ∣DT∣=∣MN∣+∣DK∣. If ∣MP∣=2⋅∣KN∣, prove that ∣AT∣=∣MC∣. geometrymidpointsperpendicular