SHARYGIN 2019 Problem 10

Let $N$ be the midpoint of arc $ABC$ of the circumcircle of triangle $ABC$, and $NP, NT$ be the tangents to the incircle of this triangle. The lines $BP$ and $BT$ meet the circumcircle for the second time at points $P_1$ and $T_1$ respectively. Prove that $PP_1 = TT_1$.