n-regular polygon inscribed the circle

Angles, Circle
In the Input field enter x^2 + y^2 = 36. Show the slider n( from 3 toi 1500, ingradient 1). Construct the point M (6cos 360°/n, 6 sin 360°/n) and segment [B,M]. Then n-regular polygon with side BM.
Why is chosen M (6cos 360°/n, 6 sin 360°/n)? What properties you know about regular polygon? What happens when the number of sides is increased?