construct a square without a ruler

On way to do this is to start by constructing the middle point of your segment like this:

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Then you will easily have the middle of your square like this:

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And you know can have a circonscrit circle for your square, and constructing the square is finally possible!

Edit.

Since you asked for it, I have made a few more drawings to illustrate how to construct the point $O$ from where we left it.

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Where the last circle has for radius $CF$ and for center $A$.

Edit 2.

Since more details were requested, here is how to finish the proof once $O$ has been constructed.

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The key to solve this problem is how to construct $\sqrt{2}$. enter image description here

Tags:

Geometry

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