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2019 T13: A Peculiar Laser

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January 27, 2019
2019team

Problem Statement

Points AA, BB, and CC lie in the plane such that AB=13AB=13, BC=14BC=14, and CA=15CA=15. A peculiar laser is fired from AA perpendicular to BC‾\overline{BC}. After bouncing off BCBC, it travels in a direction perpendicular to CACA. When it hits CACA, it travels in a direction perpendicular to ABAB, and after hitting ABAB its new direction is perpendicular to BCBC again. If this process is continued indefinitely, the laser path will eventually approach some finite polygonal shape T∞T_\infty. What is the ratio of the perimeter of T∞T_\infty to the perimeter of △ABC\triangle ABC?
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