Playing a blu-ray on a 2010 iMac

As you've probably guessed from the title, I'm trying to play several blu ray discs on my 2010 iMac (it has a slot on the right side, where I can play CDs and DVDs with no problem).

I know that Apple doesn't have blu ray software to play the discs, but I already have the apps VLC And Leawo Blu-ray Player. My issue at the moment is that I'm placing the blu ray disc into the DVD slot, it whirs for a bit (and makes some horrifying sounds), then force ejects it. Even with the applications open, it still force ejects the disc.

Any ideas on what I can do (because I really don't want to have to get an external drive)?