Although... maybe there's an easier way than inscribing a triangle inside the circle and then a circle inside the triangle. ;-P

Well, along the way we proved that the smaller circle's radius is half the size of the larger one's. So to construct it without the triangle, you'd just make a circle, draw a radius, and then draw the smaller circle so its perimeter intersected that first radius exactly half way.

Components of problem solving - like picking which length to set as the 'unit' of measurement are relevant not only in math, right?

Oh yeah. "What do I measure and how?" is perhaps the biggest practical recurring problem in my life.