Squaring the circle

Is it possible to do the impossible? Let’s draw a square where the corners is attached to the long leg of each angle, and then draw a circle which is attached to the 90 degree corner of each angle. From the beginning the circle surrounds the square, but as the transformation occurs and the angles start separating the relationship between the square and the circle changes. They are passing through each other, as the circle diminishes in size and the square grows, though still sharing the same center point. It is like two people meet on the same step as one is going up the stairs and the other one is going down, they are bound to meet somewhere, no? Meaning that at one point their circumference and area should be exactly equal. They meet in infinity.

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