QC Practice Problem Made me Cry from Confusion

GRE Quant Problem Solving
1

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Hi all - hoping this screenshot uploaded correctly. This problem was discussed in the recorded session I just watched for Geometry.

Greg’s explanation was to maximize the possible area of the quadrilateral within the square by moving points B & D down to form a square, which would create an area of 50 and make the problem have an answer of D.

For me, I’m so confused because I can’t see any reason why we’d be allowed to assume that a line drawn from A to C is actually the diameter of the circle. Nothing is specified in the question about whether or not the distance from A to C crosses the center of the circle. If I’m not mistaken, isn’t that the only scenario wherein his strategy is possible?

Shouldn’t this be D simply from the realization that we can’t verify if the distance from A to C is actually the diameter?

Thanks for any input & I hope I’m not the only one who got tripped up by this one.

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this is Cyclic quad. so, I think we can say connecting A to C will give us diameter but I will tag @Leaderboard to confirm it

3

That isn’t correct. The quadrilateral is cyclic, but that doesn’t mean that AC is a diameter as point C can still be moved.

That is not a bad place to start, but it isn’t enough. The reason is that there is always a chance that the maximum possible area of the quadrilateral is less than 40. In that case, the answer would end up as B, and not D. The reason Greg made the quadrilateral a square is to look for extremes.

4

OHHHHHH - and then the case in which it was a square was one where the diagonal of the square did, indeed, pass through the center, making it a diameter.

Okay, got it - thank you so much for clarifying. I got stuck because in the example, he only mentioned moving B & D and forgot to realize that A & C could be moved (in theory) to create a square.

Thank you