PLT AND INSTRUCTOR IN SMA SINGLE HAD NMAC WITH SMA TWIN AT 9500 MSL OVER LAKE TAHOE.

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ON A TRAINING FLT FOR A HIGH DENSITY ALT CHKOUT FROM O56 (GNOSS FIELD) TO TVL AND TRK WE HAD BEEN CRUISING AT 9500 FT (SAC ALTIMETER 29.93 APPROX) WITH FLT FOLLOWING FROM ZOA. WE HAD JUST RECEIVED THE TVL WX FROM FLT WATCH AND RESET THE ALTIMETER TO TVL 30.31 APPROX AND RETURNED TO ZOA. THEY THEN TERMINATED OUR RADAR SVC AS WE WERE APCHING ECHO SUMMIT AND DIRECTED US TO TVL TWR. WE WERE STARTING DSCNT OUT OF 9800 FT (DUE TO ALTIMETER CHANGE) AND WERE TALKING TO THE TWR WHEN THE PRIVATE PF MADE AN ABRUPT R TURN APPROX 40 DEG BANK AND 40 DEG HDG CHANGE. I HAD BEEN CHKING SOME INFO IN THE AFD AND LOOKED UP TO SEE A LIGHT TWIN OUT THE L SIDE OF THE PLANE IN LEVEL FLT AT 9500 FT ON HDG EXACTLY OPPOSITE WHAT OURS HAD BEEN (WE HAD BEEN HDG O46) SEPARATION WAS LESS THAN 10 FT VERT AND LESS THAN 100 HORIZ. I DON'T THINK THE OTHER PLT EVER SAW US AS HE DIDN'T SEEM TO TAKE ANY EVASIVE ACTION. SINCE HE WAS WITHIN 3000 FT AGL TECHNICALLY HE WASN'T AT AN IMPROPER ALT FOR HIS DIRECTION OF FLT. HE MAY HAVE BEEN OVER THE LAKE AND COME AROUND THE MOUNTAINS TO THE N OF OUR POS OR HE MAY HAVE BLENDED IN WITH CLOUDS NE OF OUR POS +/- 15 NM (HIS PLANE WAS WHITE). CLOUD BASES APPROX 9000 MSL ESTIMATED. CENTER NEVER RPTED ANY TFC IN THE AREA BUT THEY MAY NOT HAVE SEEN HIM IN THE TAHOE BASIN.