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Question

Let AA₁ A2 A3 be an equilateral triangle with unit side length. For

k = 1, 2, and 3, let B be the point on the boundary of AA₁ A2 A3

located 1/3 unit away from A, in the clockwise direction and let Ck

be the point on the boundary of AA₁ A2 A3 located 1/3 unit away from

Ak in the counterclockwise direction. What fraction of the area of

AA₁A2A3 is the area of the intersection of AB₁ B2 B3 and AC1C2C3?

Express your answer as a fraction in simplest form.

Fig: 1