there are nine points on or inside the unit square.prove that u will always find three points, which consist a triangle with area not greater than (1/8)

Question

hartnn · Answer

what i did:
since the nine points need to be farthest from each other to get the max value of area, one possible configuration is shown in diagram. then it can easily be shown that the are of that 45-45-90 triangle is 1/2(1/2)(1/2) = 1/8 which is max.
but i want some alternative general approach , if any.
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