IrMO 2013 Problem 3

The altitudes of a triangle $\triangle ABC$ are used to form the sides of a second triangle $\triangle A_1B_1C_1$ . The altitudes of $\triangle A_1B_1C_1$ are then used to form the sides of a third triangle $\triangle A_2B_2C_2$ . Prove that $\triangle A_2B_2C_2$ is similar to $\triangle ABC$ .