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24 October 2018, 17:16 | Updated: 24 October 2018, 17:20
The disappearance of mother-of-five Sarah Wellgreen is being treated as a "potential murder", according to police.
The 46-year-old was last seen in the Bazes Shaw area of New Ash Green, Kent, where she lives, on October 9 and she has not been in contact her family since.
Her car was at her home address and there have been no transactions on her bank or credit cards, Kent Police said.
A man in his 30s was arrested on October 16 and was released on bail pending further inquiries until November 16.
She lived in Kent but worked as beauty therapist in Portsmouth on some days of the week.
Detective Superintendent Paul Fotheringham said: "We are investigating the disappearance of Sarah.
"It is entirely out of character for her to go missing and, having conducted extensive inquiries and searches, this case is now being treated as a potential murder.
"Sarah has disappeared without a trace, the only item missing from the home is her black iPhone 4.
"Officers have conducted extensive searches in New Ash Green and surrounding rural areas.
"While we continue our investigation and inquiries, I would urge anybody who saw anything suspicious in the New Ash Green area at around the time Sarah went missing, that is overnight from the evening of Tuesday 9 October into the morning of Wednesday 10 October, to contact us."
About 200 people volunteered to help police carry out searches in the area near Ms Wellgreen's home over the weekend.
Mr Fotheringham said: "We have experts with specialist technology and forensic scientists working with us to try and find Sarah.
"Residents, businesses and landowners in the rural areas around New Ash Green are asked to check their outhouses, and areas surrounding their properties.
"We are particularly interested to hear from anyone with fixed CCTV cameras within a five-mile radius of New Ash Green, whether this is residential or commercial CCTV, to come forward.
"Likewise, anyone who was out on the evening of 9 October to the morning of 10 October in that five-mile area who has dashcam in their vehicle, please contact us.
"We are also appealing to those living and working in the area bordered by the A2, M25, Meopham, Cobham, Horton Kirby and Darenth to check their sheds, outbuildings and areas of rough ground or woodland for any sign of Sarah.
"Dog walkers and anyone out in rural areas should also call us if they see anything that seems suspicious.
"If you think you may have seen Sarah or something suspicious but are not sure, please do not hesitate to call and let us know.
"I'd like to take this opportunity to thank those who have already called us, assisted with searches or sent messages of support to family who have been badly affected by Sarah's disappearance."
She is white, around 5ft 7in tall, of medium build, with green eyes and straight brown shoulder-length hair.
Detective Superintendent Paul Fotheringham said "She'd just had a new job offer she was looking forward to.
"She has spoken to friends about looking forward to the future and, most significantly, she has now missed one of her children's birthdays."