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Part of 1997 Baltic Way

Problems(1)

Infinite sum of the angles made by the points A_i,B_i

Source: Baltic Way 1997

1/28/2011
On two parallel lines, the distinct points A1,A2,A3,…A_1,A_2,A_3,\ldots respectively B1,B2,B3,…B_1,B_2,B_3,\ldots are marked in such a way that ∣AiAi+1∣=1|A_iA_{i+1}|=1 and ∣BiBi+1∣=2|B_iB_{i+1}|=2 for i=1,2,…i=1,2,\ldots . Provided that A1A2B1=αA_1A_2B_1=\alpha, find the infinite sum ∠A1B1A2+∠A2B2A3+∠A3B3A4+…\angle A_1B_1A_2+\angle A_2B_2A_3+\angle A_3B_3A_4+\ldots
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