OCILLA, Ga. -- Authorities announced Thursday they have arrested a man on murder charges in the disappearance of a high school teacher in rural south Georgia more than 11 years ago.

Ryan Alexander Duke was being held in the Irwin County jail days after investigators received a tip linking him to Tara Grinstead, a teacher and former beauty queen missing since October 2005. CBS News’ “48 Hours” investigated the case in the episode, “Stolen Beauty.”

WATCH: “48 Hours:” Stolen Beauty

“We did find the person that was responsible for Tara’s death,” J.T. Ricketson, an agent with the Georgia Bureau of Investigation, said at a courthouse news conference in Ocilla, about 165 miles south of Atlanta.

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Duke had attended Irwin County High School, where Grinstead taught history, about three years before she vanished, Ricketson said. He declined to comment on how they knew each other or a motive.

The search for the missing woman’s remains continues, reports CBS affiliate WGCL.

Ryan Duke GBI via WGCL

Connie Grinstead, the missing woman’s stepmother, told reporters she thanked God “for answered prayers.”

“We always believed that it would be solved,” she said, reading a statement at the courthouse news conference. “We just did not know when.”

It was not immediately known if Duke, 33, had a defense attorney.

Grinstead was 30 when she was last seen Oct. 22, 2005. The former Miss Tifton 1999 had spent the day helping contestants in a Miss Sweet Potato pageant in nearby Fitzgerald and then attended a cookout with friends in Ocilla. She was reported missing two days later when she failed to report to work.

Her house was found locked, with her cellphone inside. Her dog and cat were home and her car sat parked in the driveway. But Grinstead’s purse and keys were gone. A latex glove — the type worn by police officers and medical workers — was found in her front yard.

“I did have kind of a gut feeling that something was wrong,” Ocilla police chief Billy Hancock told “48 Hours” in 2008.

Police classified Grinstead as a missing person, saying there was no evidence she had been abducted. Still, authorities said they also couldn’t rule out foul play.

An outpouring of support followed in the farm community of Ocilla. Volunteers searched the area and set up a Tara Command Center with a telephone tip line and a website, www.findtara.com. Rewards of $100,000 were offered for Grinstead’s safe return or for information leading to an arrest and conviction if she was harmed.

Family members appeared on nationally televised crime shows to plead for information. Still, the case stumped investigators for more than a decade as years passed with no sign of Grinstead’s whereabouts and no arrests.

“I believe there is a piece of the puzzle that is missing,” Connie Grinstead told “48 Hours” in 2008. “And when that piece of information comes in, it will lead us to the answers of what happened to Tara.”

Ricketson gave no details Thursday as to how investigators linked Duke to Grinstead. He said a person, whom he declined to name, approached authorities with a tip days earlier.

“This gentleman (Duke) never came up on our radar through the investigation,” Ricketson said. Asked if more arrests were possible, he said, “That’s a very good question. Again, we have several more interviews to do.”

A probate judge in Grinstead’s home county declared her dead at her father’s request in 2010, more than five years after she vanished.

Police chased numerous leads that went nowhere. A Georgia man posted a YouTube video in 2009 claiming to have killed 16 people, including a “beauty queen” whose description matched Grinstead’s. But the video turned out to be a hoax.

The Irwin County sheriff in 2011 searched the area of a bridge crossing a creek after receiving a tip, but found nothing. In 2015, investigators acting on another tip drained a pond in Ben Hill County but later said they found nothing useful to the case.

The Georgia Bureau of Investigation launched an investigation with help from the local police and sheriff’s departments. The GBI interviewed an ex-boyfriend who had dated Grinstead for six years, as well as other male friends she had, but no one was charged.

“So many people have been hurt by this,” Grinstead’s stepmother said. “We hope with time this community can have closure and start to heal from this.”