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It seems that is was not a secret that Putin has a home there and that he was on holiday. The public knew this...The Kremlin’s Choice for Chechnya - 23 August 2004

During the short visit--state news agencies reported that Putin arrived in Tsentoroi around 7:30 a.m. and was back at his Black Sea holiday residence near Sochi, where he has been for a week, by 11 a.m.--Putin’s comments were broadcast on state television. "We lost a sincere, manly, talented, and exceptionally decent person,” he said of Kadyrov. “He had no aim other than to serve his people.”

Do a Google picture search for Sochi and you will see it would not be that hard to down a plane in Sochi.

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Here is one from August 22nd letting the world know Putin was in Sochi.

Putin visits war-torn Chechnya

Putin is on holiday in the Black Sea resort of Sochi in southern Russia, where he later met Chechen Interior Minister Alu Alkhanov, the favourite to win next Sunday's presidential election, and Kadyrov's son Ramzan, Chechnya's vice-premier with responsibility for security.