NMAC BTWN A CESSNA 172 TURNING FINAL FROM A R BASED LEG AND ANOTHER C172 FROM A FLYING SCHOOL PASSING ON A R DOWNWIND LEG. NO EVASIVE ACTION TAKEN DUE TO THE LAST SIGHTING OF THE OTHER ACFT.

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FLYING OUR CESSNA 172 WESTWARD INBOUND TO SAN CARLOS ARPT FROM THE E SIDE OF THE SAN FRANCISCO BAY; WE CALLED THE TWR OVER THE COMMON RPTING POINT COYOTE HILLS. SAN CARLOS ARPT IS A TWR CTLED CLASS D AIRSPACE. THE SAN CARLOS TWR CTLR ACKNOWLEDGE OUR CALL SIGN AND ASKED FOR AN IDENT. WE RESPONDED WITH AN IDENT FROM OUR XPONDER AND WERE GIVEN THE NORMAL INSTRUCTIONS TO RPT THE CEMENT PLANT ON THE W SHORE OF THE BAY FOR A R TFC BASE ENTRY FOR LNDG ON RWY 30. WE CROSSED THE BAY AND RPTED THE CEMENT PLANT AT TFC PATTERN ALT OF 800 FT. ANOTHER CESSNA 172 TO OUR R ON R TFC DOWNWIND WAS INSTRUCTED BY THE TWR CTLR TO FOLLOW US. THE OTHER CESSNA 172 IS FROM ONE OF THE FLT SCHOOLS AT SAN CARLOS ARPT. THE PLT OF THE OTHER CESSNA RESPONDED THAT HE DID NOT HAVE US IN SIGHT AND WAS 'LOOKING.' THE TWR CTLR THEN GAVE US THE VERBAL '#1 CLRED TO LAND.' THE DISTANCE FROM THE CEMENT PLANT TO THE FINAL APCH PATH IS ABOUT 1 1/2 NM. OUR AIRSPD WAS 80 KTS. SO IT ONLY TAKES ABOUT 1 1/4 MINS TO REACH THE FINAL APCH PATH ONCE XING OVER THE CEMENT PLANT. WE PUT IN 10 DEGS OF FLAPS AND REDUCE THE PWR TO INITIATE OUR DSCNT AND TURN R ONTO THE FINAL APCH PATH. WE HAD JUST DSNDED THROUGH 700 FT AND WERE ABOUT TO TURN R ONTO FINAL WHEN THE OTHER CESSNA 172 CROSSED DIRECTLY IN FRONT OF US FROM OUR R TO OUR L. WE ESTIMATED THAT HE WAS ABOUT 40 FT ABOVE US AND LESS THAN 100 FT IN FRONT OF US. THIS SCARED US TO NO END. IN OUR OPINION WE HAD COME EXTREMELY CLOSE TO A MIDAIR COLLISION WHILE ON OUR BASE LEG TO FINAL AS THE OTHER CESSNA CROSSED OVER BASE ALMOST IN LINE WITH THE FINAL APCH PATH. WE IMMEDIATELY RADIOED THE TWR WHAT HAD HAPPENED. THERE WAS NO RESPONSE FROM THE CTLR. THE PLT IN THE OTHER CESSNA CALLED TO SAY THAT HE WAS 300 FT ABOVE US. HE WAS NOT. HIS POS WAS NEARLY OUTBOUND IN THE OPPOSITE DIRECTION ON THE FINAL APCH PATH. AFTER A FEW SECONDS; THE CTLR INFORMED US THE OTHER ACFT WAS ABOVE US AND ONCE AGAIN CLRED US TO LAND. WE PROCEEDED TO LAND SAFELY WITHOUT FURTHER INCIDENT. AS WE TAXIED TO OUR TIE DOWN SPOT; WE SAW THE OTHER CESSNA ON FINAL APCH. IN OUR OPINION THERE WAS NO WAY HE COULD HAVE MADE A NORMAL BASE ENTRY TO FINAL. IT IS OUR OPINION THAT THE PLT OF THE OTHER CESSNA MUST HAVE MADE A 180 DEG TURN ONTO FINAL FOR HIS LNDG. WHEN WE WERE CLRED #1 FOR LNDG BY THE TWR CTLR; WE ASSUMED THE AIRSPACE ALONG BASE AND ALONG FINAL AND THE RWY WERE OURS; CLR OF ALL OTHER TFC. AFTER ALL; THIS IS A CTLED CLASS D AIRSPACE AND WE WERE CLRED FOR LNDG; AND SHOULD EXPECT NO OTHER ACFT IN THAT SAME AIRSPACE. THERE WAS NO TFC ALERT WARNING GIVEN BY THE CTLR TO EITHER ACFT. THE PLT OF THE OTHER CESSNA DID NOT ACKNOWLEDGE THAT HE HAD US IN SIGHT UNTIL THE MIDAIR NEAR MISS OCCURRED. WE ASSUME THE OTHER PLT MAY HAVE BEEN A STUDENT PLT; NOT FAMILIAR WITH PROCS AND LANDMARKS AT SAN CARLOS ARPT. THE OTHER PLT SHOULD HAVE WIDENED HIS DOWNWIND LEG OUTWARDS TOWARDS THE CEMENT PLANT ANTICIPATING FOLLOWING BEHIND US INBOUND ON BASE. HE DID NOT; BUT INSTEAD FLEW TO THE NORMAL BASE TO FINAL TRANSITION POINT. IN THIS INSTANCE; THE TWR CTLR SHOULD HAVE GIVEN FURTHER INSTRUCTIONS TO THE OTHER PLT; TO ENSURE ACFT SEPARATION; ONCE HE STATED THAT HE DID NOT HAVE US IN SIGHT. HOWEVER; NO SUCH ADDITIONAL INSTRUCTIONS WERE GIVEN TO THE OTHER PLT. THE LESSON HERE IS; EVEN THOUGH YOU ARE CLOSE IN ON BASE AND CLRED TO LAND BY THE ARPT TWR CTLR; KEEP YOUR SITUATIONAL AWARENESS ALIVE AND LOOK FOR AND EXPECT OTHER TFC TO BE IN YOUR AIRSPACE AS YOU APCH FINAL FOR LNDG; EVEN THOUGH YOU ARE FLYING IN A CTLED ARPT CLASS D AIRSPACE.