ÖMO 1989 Problem 4

We are given a circle $k$ and nonparallel tangents $t_1,t_2$ at points $P_1,P_2$ on $k$ , respectively. Lines $t_1$ and $t_2$ meet at $A_0$ . For a point $A_3$ on the smaller arc $P_1 P_2,$ the tangent $t_3$ to $k$ at $P_3$ meets $t_1$ at $A_1$ and $t_2$ at $A_2$ . How must $P_3$ be chosen so that the triangle $A_0 A_1 A_2$ has maximum area?