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Five Congruent Equilateral Triangles

Source: 2012 AIME II Problem 13

March 29, 2012
trigonometryvectorsymmetrytrig identitiesLaw of Cosinescomplex numbersAMC

Problem Statement

Equilateral △ABC\triangle ABC has side length 111\sqrt{111}. There are four distinct triangles AD1E1AD_1E_1, AD1E2AD_1E_2, AD2E3AD_2E_3, and AD2E4AD_2E_4, each congruent to △ABC\triangle ABC, with BD1=BD2=11BD_1 = BD_2=\sqrt{11}. Find ∑k=14(CEk)2\sum^4_{k=1}(CE_k)^2.
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