Ah, you need something different, then what I imagined.

Do you want a line that emanates from the center of the circle (like a radar display)

or do you want a curved line that travels around the edge of the circle?

The first one is easy to do, and is not nearly as complicated as drawing a circle.

I have a different routine for doing the second (it's a variant of drawcircle that accepts a start-angle and end-angle) - you still need to keep theta at 45 degrees.