72-Concurrency on the Tucker circle

Let a Tucker circle cut sidelines of given triangle $ABC$ at $A_b,A_c, B_c,B_a,C_a,C_b$. If $A_2A_bA_c, B_2B_aB_c, C_2C_aC_b$ are three similar isosceles triangles then $AA_2BB_2CC_2$ are concurrent