C210 PILOT WITH INSTRUCTOR ABOARD IS DISTRACTED DURING APPROACH AND MAKES GEAR UP LANDING.

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WE TOOK OFF AROUND XA45; AFTER ABOUT 10 MIN DELAY BECAUSE OF TFC AND OTHER RELEASES AHEAD OF US. HE REACHED 1000 FT TURNED DOWNWIND AND LEVELED OFF. ON DOWNWIND ABEAM; I LOOKED AT PLT'S HAND ON THE GEAR LEVER; WE GOT EXTENDED AND THEN WE GOT CALLED FOR A BASE FROM THE TWR. PLT RESPONDED; STARTED TO TURN BASE AND AT THAT POINT I REMINDED HIM OF THE GUMPS; AND ACTUALLY CALLED THEM OUT FOR HIM. THE MIXTURE WAS PUSHED FORWARD AND THE FIRST NOTCH OF FLAPS WAS LOWERED. HE WAS ON FINAL A LITTLE FAST AND I REMINDED HIM OF THE SPD FLAPS AND GUMPS. HE CONFIRMED FLAPS DOWN FULL AND GEAR; OR UNDERCARRIAGE; AND PROCEEDED TO LAND. ON SHORT FINAL I LOOKED AT THE GEAR INDICATOR LAMP; BUT I COULD NOT SEE IT BECAUSE HIS HAND WAS BLOCKING MY VIEW; HE WAS MANIPULATING THE FLAPS LEVER. HE WAS A LITTLE L OF THE CTRLINE AND REMINDED HIM OF THAT. HE CORRECTED AND HE ROUNDED OUT; FLARED AND I HEARD A METALLIC/UNUSUAL NOISE. WE TOUCHED DOWN SMOOTHLY AND THEN IT BECAME CLR THAT THE GEAR WAS NOT DOWN. DURING THE FINAL; OR ANY OTHER TIME INFLT; WE NEVER GOT A GEAR UP HORN/BUZZER WARNING. A FSDO PERSON SHOWED UP AND ASKED FOR A RPT. WE BOTH COMPLIED. NOBODY WAS INJURED DURING THE INCIDENT. WE RELIED ON SOME OF THE SYS TO WARN US IF A PROB EXISTED; BUT WE COULD AND SHOULD HAVE VERIFIED IF GEAR WAS DOWN AND LOCKED BY USING OTHER PROCS.