Connect external screen iMac 27" late 2012

I'm having trouble connecting an external monitor to my IMac (27 inch, late 2012). I have used both Mini display port VGA and mini display port - HDMI cable to connect the devices. Both of these options work with other MacBook Airs (ie, they display on the external screen).

I use a 27 "monitor with maximum resolution 1920 x 1080 / FHD. When the IMac is connected, it still says that there is no signal.

According to the IMac specifications, it says that

"Simultaneous support for full resolution on the built-in screen and up to 2560 x 1600 pixels on an external 30-inch screen". Does this mean there must be a 30 inch screen? Or does it work with 27 inch screen too?