If you have a circle with center c how do you located the vertices of a of a square inscribed in circle c

You'd either have to provide a value for the circle radius, r, or use the variable "r" for that purpose.

Draw a circle of radius r. In the first quadrant, draw a sample radius from circle center c to the circle. The angle between this radius and the x-axis is 45 degrees. Thus, you can find the x - and y-coordinates of one vertex using the following formulas:

x = r*cos 45 deg

y = r*sin 45 deg