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Construct with a ruler and compass a square, given one point from each side.

Square Deal

I was reading the answer to Square Deal, and I do not understand how the rest is easy to solve. Could someone help me understand? I don't see the square.

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@Freddy, if it's not a Euclidean space, then what's a square? – Gerry Myerson Jan 20 '13 at 10:15
Ah, Ok, I overlooked it. – 007resu Jan 20 '13 at 10:57
It would be useful to include the partial solution given in the link, both for the convenience of readers here, and to prevent link rot. – Travis Sep 16 at 3:24

1 Answer 1

up vote 6 down vote accepted

Connect $A$ and $C$ and draw a perpendicular from $B$ to this segment. Now construct $D’$ on this perpendicular such that $AC = BD’$. $DD'$ is one side of the square. (This construction is already given in the link provided)

Now to complete the square, draw perpendiculars from point $A$ and $C$ to the line $DD'$. And then draw a line passing though $B$ parallel to $DD'$.

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