In the first case, an arc can be defined by selecting two points - the first being the center of the circle that the arc is on, and the second being a radial point on this circle. When we click on the arc tool, a dialog box will pop up asking us for an initial and terminal angle for this arc (measured in degrees in relation to the horizontal). After setting these values the arc will appear.
In the third case an arc can be defined by selecting three points. These three points will define a unique circular arc, starting with the first point selected, passing through the second, and ending with the third. (Note: This last construction depends on the parallel postulate and thus is not available in Hyperbolic or Elliptic Geometry)