Here are two methods:
1) With the object of group to be duplicated still selected, hold down the command key and click (using a modifier if so desired) at the point that you want the duplication centered around. Now when you go to Polar Duplicate the X and Y location of the point that you have clicked will automatically entered in the dialog.
2) You can reposition the zero (x=0,y=0) point to the x and y center of duplication. To reposition the zero point click in the small box in the upper-left most corner of the ruler (it shows the active ruler number) and drag it onto your drawing. Your arrow will now point to crosshairs across your screen. Wherever you release the mouse is where the new zero point will be. You may also specify this point using a modifier.
For example, you could reposition the zero point to the center of a circle using the center on modifier.
To return the zero point, just click on the active ruler number again.