Let ABC be an acute triangle with AB<BC. Let I be the incenter of ABC, and let ω be the circumcircle of ABC. The incircle of ABC is tangent to the side BC at K. The line AK meets ω again at T. Let M be the midpoint of the side BC, and let N be the midpoint of the arc BAC of ω. The segment NT intersects the circumcircle of BIC at P. Prove that PM∥AK. geometryincirclecircumcircleparallelTSTincenter