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2014 Guts #25: Extending Trisectors to form a Hexagon

Source:

August 26, 2014
geometry

Problem Statement

Let ABCABC be an equilateral triangle of side length 66 inscribed in a circle ω\omega. Let A1,A2A_1,A_2 be the points (distinct from AA) where the lines through AA passing through the two trisection points of BCBC meet ω\omega. Define B1,B2,C1,C2B_1,B_2,C_1,C_2 similarly. Given that A1,A2,B1,B2,C1,C2A_1,A_2,B_1,B_2,C_1,C_2 appear on ω\omega in that order, find the area of hexagon A1A2B1B2C1C2A_1A_2B_1B_2C_1C_2.
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