RUMORS of an explicit home video showing Christie Brinkley’s slimy hubby Peter Cook having sex with his curvy teen office worker Diana Bianchi have made the rounds for months, and now Page Six can reveal the truth – it does exist.

Yesterday, we were shown a series of stills from a video depicting Cook and Bianchi, both nude, having sexual intercourse on a brown love seat. They also show Bianchi performing a sizzling striptease down to a pair of black, G-string panties and then to her birthday suit as Cook holds his crotch.

Another shows Cook resting his head on Bianchi’s buttocks. It appears the tape was made at Cook’s Southampton architectural office without Bianchi’s knowledge. But other stills that are apparently not from the video show Bianchi willingly posing topless.

In July, Brinkley settled her nasty divorce with the philandering Cook – who detonated their 10-year marriage with his affair with then-18-year-old Bianchi – for just $2.1 million of her $60 million fortune. She also won full custody of their kids. Cook, who confessed to a $3,000-a-month online porn habit, doled out $300,000 to Bianchi in a legal settlement that kept her mum and prevented a likely sex-harassment lawsuit.

One theory why Cook settled for so little is that Brinkley found the pictures on his computer and used them as leverage. Brinkley’s lawyer Robert Cohen said: “Nothing about Peter Cook’s behavior shocks us. We don’t know anything about this tape. We never saw it and we never heard about it. Christie’s concern is for the sake of her children and she hopes this video is kept private.”

Bianchi’s lawyer, Joe Tacopina, said she may sue Cook over the video. “We are now going to review, and begin weighing our legal options, for Diana,” he told The Post’s Dan Mangan. Cook declined to comment, but a source close to him said: “He has no knowledge that any such material exists, but it is well known that Cook and Bianchi had a consensual affair, so anything is possible.”