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Bermuda Triangle

Source: 2016 AIME II #5

March 17, 2016
AMCAIMEAIME II2016 AIME II2016 AIME II Problem 5geometryright triangle

Problem Statement

Triangle ABC0ABC_0 has a right angle at C0C_0. Its side lengths are pairwise relatively prime positive integers, and its perimeter is pp. Let C1C_1 be the foot of the altitude to AB‾\overline{AB}, and for n≥2n\geq 2, let CnC_n be the foot of the altitude to Cn−2B‾\overline{C_{n-2}B} in △Cn−2Cn−1B\triangle C_{n-2}C_{n-1}B. The sum ∑n=1∞Cn−1Cn=6p\sum\limits_{n=1}^{\infty}C_{n-1}C_n = 6p. Find pp.
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