I think I figured out the best possible argument. If this has already been brought up... well... it's worth bringing up again.
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The arctic circle is 66°33' N. It is 10,975 miles in circumference. Measure the circumference yourself if you don't believe this.

I convert 66°33' to a decimal, which rounded would be 66.5
The latitude of the equator is 0°.
66.5-0=66.5
So the difference in latitude between the arctic circle and the equator is 66.5
One degree of latitude is 69 miles.
69*66.5=4588.5
The distance between the arctic circle and the equator is approximately 4588.5 miles.
The circumference of the equator is 24901.5 miles. Once again, if you do not believe this you can measure it yourself.
The antarctic circle is at 66°33' S. Also approx. 4588.5 miles from the equator. This is found using the exact same reasoning as before.
This should be accepted by people on both sides of this argument. This data is consistent with the earth being flat with the north pole at the center, and with the earth being round. It's this next part that would prove one or the other correct.
Here's the fun part.
If the earth is FLAT, you would expect the antarctic circle to have a larger circumference that the equator. Quite a bit larger. Right?
If the earth is NOT FLAT, but is in fact a 3d spherical shape as is the accepted theory, you would expect the antarctic circle to have the same circumference as the arctic circle.
Now, since the round earth theory has been tested and reviewed by many members of the scientific community over several hundred years, the burden of proof lies with the challenging theory. The flat earth. Measure the circumference of the antarctic circle.
If you get anything close to 39,300 miles, than you have an argument. That is what you would expect for a circle with a radius 4588.5 miles longer than a circle with a circumference of 24901.5 miles.
If you get anything close to 10,975 miles; congratulations. You have just rediscovered that the earth is a sphere.
NOTE: I only chose the arctic and antarctic circles because they are convenient. Not too close from the poles, not too close to the equator.
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Any questions?