Joanna Yeates may have been held captive before her murder

After detectives confirmed yesterday that Joanna Yeates was strangled, her father said that he believes the police know more about the landscape architect's death than they are telling the family.

Ms Yeates, 25, who was missing for more than a week before she was found – frozen and covered in snow, by dogwalkers on Christmas morning – had died several days before as a result of "compression of the neck", a post-mortem examination has revealed. Her body was recovered about three miles from her flat in Bristol.

David Yeates, 63, told the Southern Daily Echo: "We are sure the police know more about what happened than they are telling us, but at the moment we are not questioning them because we feel they are doing their best."

His comments came as detectives officially opened a murder inquiry and said that they were keeping an "open mind" as to possible theories or motives. Many unanswered questions remain.

"We now know how she died," said Detective Chief Inspector Phil Jones, of Avon and Somerset Police. "What we have to do next is find out why she was killed and who was responsible."

Ms Yeates was last seen on 17 December when she left friends at the Ram pub to walk to her home in the Clifton area of Bristol. She then went to a Tesco store where she was captured on CCTV buying a pizza.

Yesterday it was revealed that she had also visited a Bargain Booze store next door, where she bought a small bottle of cider.

She is then believed to have returned to the flat she shared with her boyfriend on Canynge Road – her coat, purse, mobile phone and keys were all found there, as well as a receipt for the pizza. But neither the pizza nor its packaging have been recovered. Det Ch Insp Jones was unable to say yesterday whether or not examination of Ms Yeates's stomach contents had established if she had eaten the pizza.

Given that there was no sign of forced entry to the flat, one line of inquiry officers are pursuing is that Ms Yeates knew her killer. Police are also investigating the possibility that Ms Yeates may have been held captive.

Det Ch Insp Jones reiterated that Ms Yeates's boyfriend, Greg Reardon, who raised the alarm that she was missing on 19 December after returning from visiting family in Sheffield, was being treated as a witness and not as a suspect. The officer confirmed that Mr Reardon's laptop and mobile phone had been examined, but that this was standard procedure.

Yesterday Det Ch Insp Jones said that he believed Ms Yeates's body had been dumped on the roadside verge "several days" earlier. The officer also confirmed that Ms Yeates was fully clothed when discovered, but did not rule out a sexual motive to her death.

Police are continuing to review hours of footage from the 32 CCTV cameras which monitor Clifton Suspension Bridge, the main road link between Ms Yeates's flat and where she was found.

Yesterday Mr Yeates said: "Hearing Jo had been murdered was not a surprise because we had been told to prepare for the worst."

But, he added: "I fear that whoever has done this will never hand themselves in but we live in hope that the police will catch who is responsible.

"Since hearing about her death, all sorts of things have been running through our mind and we are trying to rationalise what has happened.

"Last week was the worst of our lives and we are hoping that we will never have to go through anything like this again."

He added: "Things were made just that little bit less terrible when we saw Jo's body. It was a relief to see her again – we just said: 'Welcome back'."