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ABCD is a square. How many squares in the same plane have two or more vertices in the set {A,B,C,D} ?

 

(I know others posted this same question, but the answers they received were not correct.)

 Dec 5, 2023
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If we think of the square as being circumscribed by a circle, then there are 4 pairs of adjacent vertices of the square, each pair of which can be chosen as the two diagonals of a smaller square.

 

Therefore, 8​ squares in the same plane have two or more vertices in the set {A,B,C,D}.

 Dec 5, 2023

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