Polyfun!!! 2

Now, let's see 3 observations

1. All regular polygons are cyclic.

2. Connecting 2-opposite vertices in a regular polygon with even number of vertices gives us a diameter of the circumcircle.

3. Angle in a semicircle is 90°.

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Now, there are 500 possible diameters and 2 of our vertices are ends of it. Now, the $3 ^{rd}$ vertex and $4^{th}$ vertex have to lie on opposite sides of the diameter (try to prove why), and selecting the $3^{rd}$ vertex automatically decides the $4^{th}$ one.

Now, we have to select the $3^{rd}$ vertex. This has 497 possible vertices on one side of the diameter (Excluding the ends of diameter and the vertices adjacent to it). Also, our combination leads to an identical rectangle for each rectangle (A rectangle has 2 diagonals).

So, number of combinations is equal to $\boxed{\frac{500 × 497}{2} = 124250}$