MathDB
SMT 2021 Geometry #4

Source:

August 9, 2023
geometry

Problem Statement

△A0B0C0\vartriangle A_0B_0C_0 has side lengths A0B0=13A_0B_0 = 13, B0C0=14B_0C_0 = 14, and C0A0=15C_0A_0 = 15. △A1B1C1\vartriangle A_1B_1C_1 is inscribed in the incircle of △A0B0C0\vartriangle A_0B_0C_0 such that it is similar to the first triangle. Beginning with △A1B1C1\vartriangle A_1B_1C_1, the same steps are repeated to construct △A2B2C2\vartriangle A_2B_2C_2, and so on infinitely many times. What is the value of ∑i=0∞AiBi\sum_{i=0}^{\infty} A_iB_i?
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