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Two men posed as police officers in order to steal jewellery from an elderly woman.
The distraction burglary happened in Gresham Road, Coxheath, between 8.50pm and 9.20pm on Friday.
The suspects entered the property through the back door and told the woman, aged in her 80s, they had arrested someone for trying to burgle her home.
One man spoke to the victim as the other searched the house.
The first suspect is described as being white, aged between 20 and 29, and approximately 5ft 6ins tall with light brown hair.
The second is described as being white, aged between 30 and 39, and approximately 5ft 8ins tall with a slim build and short black hair.
Kent Police say the incident could be linked to a similar theft of jewellery and a watch from Acacia Walk, Swanley, on Monday, November 14, between 10.15pm and 11pm.
Two similar incidents were reported in Gravesend on Saturday, 26 November.
Anyone with information can call Kent Police on 01622 604100 quoting reference number YY/027720/16.