This is a problem Greg was solving in the video (Quant Misc - GRE Geometry), and in his explanation he assumed that the diagonal was AC = 10 while testing the case for a square. However, in his previous videos in the plan, he suggested not to assume anything, esp. in the QC geometry questions. For example, if it looks like a square it’s not necessarily one unless it’s mentioned that the sides are all equal or any other clue. Or if the center of a circle is not mentioned, don’t assume a line passes through it even if it looks like it does.

The way I approached this problem: the diameter is the largest chord of the circle. BD must be less than 10. CA could be or could not be the diameter. Answer: D.

Can someone please tell if my process/reasoning is correct? Thank you for your help!

As, the figures given in the Quant section are not on the scale, so you can’t say for sure BD is less than 10. it may be 10. How I approach this question is using the following facts:

the area for four-sided figure will be maximum when all the sides are the same(i.e Square) at this case that will be 50

then the area of half of the circle( i.e semicircle), in this case, is 39.26, and I can draw a similar shape even in a semicircle which means the minimum area of such shape may be less than 39 too.

The answer is D, I just arrived at the answer in a not too straightforward way, because I’ve never been good at math lol. Thanks, I appreciate your confirmation!

Yep, that’s how Greg tackled it but he assumed that AC was running through the center. But the point was definitely to account for the fact that regular shapes have maximum area.

Wow man, I’m guessing you are a math or CS graduate. Had to read three times to infer what you wrote. That’s some super astute cross checking. Thanks for your help!