Use the Fillet and No Trim function to create a fillet arc without trimming.

 

Using the Function:

1. Select No Trim from the Modify>Fillet submenu.

2. Enter a value for the radius of the arc fillet.

3. Select the first fillet entity. (You can click anywhere on the entity; you do not have to select any specific location relative to the arc radius.)

4. Select the second curve on the portion of the curve that you want to remain.

Above > An example of Fillet and No Trim