A quadrilateral that is inscribed in a circle that by dynamic process convergent to a square

Idan Tal
Circle, Square
The applet demonstrates that for any quadrilateral inscribed in a circle, by dynamic process, its convergent to a square. By connecting the midpoints of the arcs of a quadrilateral that is inscribed in a circle, we created new quadrilateral. The ruler allows the creation of a sequence of quadrilaterals, the vertices of each of which are located at the middles of the arcs of the previous quadrilateral. For each quadrilateral, the values of the angles of the new quadrilateral obtained, and their standard deviations appear on the screen. The standard deviation indeed decreases monotonically, which suggests that the angles converge to 90°.