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altitudes of a triangle form a second triangle, altitudes of second form a third

Source: Irmo 2013 p1 q3

September 15, 2018
geometrysimilar trianglesaltitudes

Problem Statement

The altitudes of a triangle △ABC\triangle ABC are used to form the sides of a second triangle △A1B1C1\triangle A_1B_1C_1. The altitudes of △A1B1C1\triangle A_1B_1C_1 are then used to form the sides of a third triangle △A2B2C2\triangle A_2B_2C_2. Prove that △A2B2C2\triangle A_2B_2C_2 is similar to △ABC\triangle ABC.
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