"Let ΔABC be inscribed in circle O. Point P is inside ΔABC, and the projections of P on the sides BC, CA, and AB are points X, Y, and Z, respectively. The second intersection point of line AP with circle O is D. Point E lies on circle O, and DE is perpendicular to BC. Let I be the midpoint of DE. Line PI intersects BC at F, and point T lies on AF such that TX is parallel to AD. Prove that line YZ bisects line TX."