How to avoid mistakes when drawing in perspective

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Let's begin with a square. A circle can be inscribed into it. I will rotate it 45 degrees, so its diagonal is horizontal. Such a diagonal can be divided into 7 parts. Let's draw those parts. These measuring units will be helpful to inscribe a circle in perspective. Here's how it works. Three and a half parts fit from the square's corner to its center. One part is very close to the circle's outline. Let's keep it in mind.

Now, I will draw a square in two-point perspective. We will now check if it is a perfect square or not. Its center is where two diagonals cross each other. From that center, there are three and a half parts to the corner. This is where the ellipse edge should be.

You can see that this ellipse touches two sides in the middle. These points are marked in green. However, two remaining points in red do not touch sides. Therefore this shape is not a square, but a rectangle.