IND Approach Controller providing OJT from an adjacent RADAR display described a loss of separation event when he realized the developmental had taken a hand off that eventually conflicted with another IFR aircraft.

Narrative

A C172 was on frequency north; northwest bound and 6;000 FT. I was completely unaware of Aircraft X. I was conducting OJT at an adjacent scope. My practice was to turn a data block blue when the aircraft checked on the frequency. When the Developmental reacted to the pending loss of separation I was stunned to see 2 targets in the vicinity. I thought I had been scanning well as there were a lot of overflights; satellite arrivals and IFR departures. After the Developmental began to take action I learned that Aircraft X was on the frequency and landing at an airport in a sector next to our airspace boundary. Had I known of this traffic I would have suggested the Developmental issue a descent to Aircraft X to resolve the conflict. I did not see the Developmental take the hand off on Aircraft X; and I do not remember him checking on the frequency. When conducting OJT at an adjacent scope I would like to see the same visual presentation on the STARS as the Developmental; same colors and hand off functions.