KöMaL 2012 B4499

Let $P$ be an interior point of an acute-angled triangle $A_1 A_2 A_3$. The points $T_i$ are such that the line segment $A_i T_i$ touches the circle of diameter $PA_{i+1}$ at $T_i$ ($i$=1,2,3, $A_4$=$A_1$). Show that $2\cdot \sum_{i=1}^3A_i T_i^2 =\sum_{i=1}^3A_iA_{i+1}^2$.