2012 AIME II Problem 13

Equilateral \triangle ABC has side length \sqrt{111}. There are four distinct triangles AD_1E_1, AD_1E_2, AD_2E_3, and AD_2E_4, each congruent to \triangle ABC, with BD_1 = BD_2 = \sqrt{11}. Find \sum_{k=1}^4(CE_k)^2.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.