BUT you can also do it with Polar [F10] and Object-Snap Tracking [F11].  Have CENter among your running Object-Snap modes, and the 45-degree multiples among your Polar angles.  Call for the BREAK command, pick the Arc, choose the First option, hover over the Arc with the cursor so that a little cross appears at its center, then hover over that cross so that it "lights up" and you can Polar-track from there in the 90-degree direction [you don't need to pick on the Arc, just establish the direction], then for the second Break point, again hover over the Arc to get the center mark, hover over that to grab it as a base point for Polar-tracking to the 135-degree direction from there.

The method I described will do it without drawing any addtional/temporary object(s).  [That's one of the main purposes of Polar/Object-snap Tracking -- you can "get to" various locations in relation to things without needing any object(s) there to snap (or Trim or Extend or whatever) to.]