2002 AIME I Problem 5

Let A_1, A_2, A_3, \ldots, A_{12} be the vertices of a regular dodecagon. How many distinct squares in the plane of the dodecagon have at least two vertices in the set \{A_1,A_2,A_3,\ldots,A_{12}\}?

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.