Question 1189905
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Let ABC be an equilateral triangle. How many squares in the same plane as ABC 
share two vertices with the triangle?
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Since the problem says nothing about possible overlaying the squares,  I will assume 
that overlaying is allowed and is not an issue.


Then each side of the triangle determines three such squares:


            - two squares on different sides of the side that share the side,


            - plus one square which has a diagonal coinciding with the side.



<U>ANSWER</U>.   &nbsp;&nbsp;In all, &nbsp;there are &nbsp;3 * 3 = 9 &nbsp;such squares.
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I answered this question assuming that squares must share their vertices with that of the triangle.