RO-TST 1991 Problem 5

In a triangle $A_1A_2A_3$ , the excribed circles corresponding to sides $A_2A_3$ , $A_3A_1$ , $A_1A_2$ touch these sides at $T_1$ , $T_2$ , $T_3$ , respectively. If $H_1$ , $H_2$ , $H_3$ are the orthocenters of triangles $A_1T_2T_3$ , $A_2T_3T_1$ , $A_3T_1T_2$ , respectively, prove that lines $H_1T_1$ , $H_2T_2$ , $H_3T_3$ are concurrent.