Drawing complex shapes in Eagle
Unlike AutoCAD or SolidWorks, there is no command in Eagle, which would break or trim lines at intersections.  

Your shape isn't very complex.  There are several options.


Find/calculate the coordinates of the intersection points.  Then draw 2 separate arcs and 2 separate lines.
Draw a rectangle.  Then change the Curve property of the sides, which will make them into arcs.