Arranging 3 letter words in a 2D matrix such that each row, column and diagonal forms a word

You are given a dictionary of 3 letter words and have to find a matrix of 3x3 such that each row, column and diagonal forms a word in the dictionary. The words in the dictionary are sorted and you can assume O(1) time for retrieving a word from the dictionary.

This has been asked as a Facebook interview question.