2 out of 3 aint bad

Discrete Mathematics Level pending

You and a friend decide to play the following game...

You draw three distinct dots inside a unit square.

Then your friend draws the biggest rectangle (with edges parallel to those of the square) she can which contains exactly two of the three dots.

With the initial three dots, you try to minimize the size of the rectangle she is able to draw.

If you play optimally, what is the area of the largest rectangle she will be able to draw containing exactly two of the three dots?

Give your answer to 3 decimal places.


Assumption: The dots are allowed to share the same \(x\) or \(y\) coordinate, but not both.

Here is a harder version of this question
Inspiration.
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