SOLUTION: Let ABC be an equilateral triangle. How many squares in the same plane as ABC share two vertices with the triangle?

Question 1189905: Let ABC be an equilateral triangle. How many squares in the same plane as ABC share two vertices with the triangle?
Answer by ikleyn(52816)   (Show Source): You can put this solution on YOUR website!
.
Let ABC be an equilateral triangle. How many squares in the same plane as ABC
share two vertices with the triangle?
~~~~~~~~~~~~~~~~~

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.

ANSWER.   In all, there are 3 * 3 = 9 such squares.

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I answered this question assuming that squares must share their vertices with that of the triangle.

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