Intersect

With this option the user can break a curve at an intersection. The two curves need to be overlapping each other for it to work.
The Selection window will open and the user will need to select two curves and select OK. In some cases, where there is more than one solution a Solution window will be displayed.

When the Solution window opens, click the left mouse button. This will display the different solution available. Use the right mouse button to select the appropriate solution.
Once the operator has accepted the solution, delete any of the curves not needed.
Below is a before and after.

BeforeAfter