Dao's blog: 36-Three perpector are collinear

If two triangle $\triangle ABC$ and $A_1B_1C_1$ are perpective; $A_2,B_2,C_2$ are intersection of three line reflection of $AB,BC,CA$ respectively on $A_1B_1,B_1C_1,C_1A_1$ then $\triangle A_2B_2C_2$ perpective with $\triangle ABC$ and $\triangle A_1B_1C_1$ . Three perpector are collinear.