You can do this without drawing any extra objects. Rotate the UCS with the 3 point option, osnap to center, to your point on the circle, and in a general direction to show Y. Set Ortho or Polar on, start the line command and use Quad Osnap to pick your starting point, or use Intersection, etc. I have quick keys set to U3 to get the UCS command set to 3 point option, and UW to go back to UCS World.
Edit: snap to the point on the circle first, then center, then another direction for Y.