Why is this relationship shown as a cycle

For rock cycle, it’s just part of the system of rocks being created and destroyed in cycles. Since it’s a model that describes formation breakdown and reformation of rocks. And of course the result is either sedimentary, metamorphic, or igneous.

I'm pretty sure there's a geometry rule for   anyways, if the triangle is equilateral, and the circle is circumscribed, the circle is outside of the triangle.  to find the area, you need the radius.  the radius should be a straight line from the center of the triangle to any of it's points.  draw lines from the center of the circle to each of the triangle points.  draw three more lines from the center to the middle of the sides of the triangle.  you should now have six separate 30-60-90 triangles inside of your original triangle. use your 30-60-90 rules to solve for the radius, then the circumference.