Can you tell us how you have the projector connected to your mac?
Do you have anything on the projectors display or is it blank?
If you move the mouse off the side of your main monitor does it show up on the projectors screen?
Int at case can you click the apple icon then open System preferences and then open Displays and let me know if the Projector is shown as an option?
If so can you see if it will allow you to enable to projector as a second monitor.
Let me know
When you get the displays menu open can you hit detect displays and let me know if anything appears on the projector as you should get a display settings window on it and you should see an arraingement dialogue on your iMacs screen so you can choose how to lay out the displays.
Let me know what happens.ThanksEric