In triangle ABC with AB=23, AC=27, and BC=20, let D be the foot of the A altitude. Let P be the parabola with focus A passing through B and C, and denote by T the intersection point of AD with the directrix of P. Determine the value of DT2−DA2. (Recall that a parabola P is the set of points which are equidistant from a point, called the <spanclass=′latex−italic′>focus</span> of P, and a line, called the <spanclass=′latex−italic′>directrix</span> of P.)