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Math Prize 2023 Problem 4

Source:

October 11, 2023

Problem Statement

Let △A1A2A3\triangle A_1A_2A_3 be an equilateral triangle with unit side length. For k=1k = 1, 22, and 33, let BkB_k be the point on the boundary of △A1A2A3\triangle A_1A_2A_3 located 1/31/3 unit away from AkA_k in the clockwise direction and let CkC_k be the point on the boundary of △A1A2A3\triangle A_1A_2A_3 located 1/31/3 unit away from AkA_k in the counterclockwise direction. What fraction of the area of △A1A2A3\triangle A_1A_2A_3 is the area of the intersection of △B1B2B3\triangle B_1B_2B_3 and △C1C2C3\triangle C_1C_2C_3?
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