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Exclusive photos show the moment a Brooklyn man found his neighbors bound by duct tape in their Bay Ridge house — right after home invaders made off with their safe containing more than $50,000 in cash and $80,000 worth of jewelry.

The victims — a 36-year-old woman, her 81-year-old father and 75-year-old mother, according to neighbors — can be seen sitting calmly with wrists and ankles bound and duct tape over their mouths, according to photos shot by neighbor Joanne Nguyen.

Nguyen’s husband, Gary Baxter, said he was “futzing around” with his model train set in the backyard of his 6th Avenue home near Bay Ridge Avenue on Monday afternoon when he heard a “big bang,” prompting Nguyen to come running to the backyard.

Through their fence, Baxter and Nguyen saw two men leave their neighbor’s back door and push “the safe out of the driveway” before carrying it to a waiting blue Jeep Cherokee occupied by a driver, Baxter said.

A quick-thinking Baxter, who was shirtless and wearing swim trunks at the time, snapped a photo of the getaway car before running into the burglarized home, where he found his visibly stunned neighbors, with duct tape over their mouths and hands, sitting on the couch.

The 36-year-old victim, who neighbors say is a single mom and who told police she lives at a different address, was duct-taped at the mouth, hands and feet by the crooks, but had already partially freed herself when Baxter ran in.

“I went in there. I see this and I say, ‘Oh crap!’ I see them all taped up,” said Baxter, whose wife snapped photos of the victims still bound as evidence for police. “I try to make the old couple just relax, just sit tight.”

Baxter then freed the victims, pulling the duct tape off them.

“As I’m taking the tape off, I’m calling the police,” said Baxter as he noted that there was a communication barrier since the family did not speak English. “I try to calm them down and take the tape off easy because they’re 80 years old, these freaking people.”

Baxter continued: “They seemed basically stunned. There was almost zero reaction … They were not hurt as far as I can tell.”

Nguyen added that she was “very nervous” and “shaking” at the sight of her neighbors.

Home surveillance video footage captured the 3 p.m. heist, and shows one of the crooks impersonating a FedEx worker and holding a package as he knocks on the front door before the two make their way inside.

Police said one of the thieves claimed to be police and flashed a shield, shouting, “Police, don’t move,” before the bandits bound the trio.

While inside, one of the thugs shoves a black safe — holding $54,000 in cash and $80,000 in jewelry — toward the younger woman, yelling at her to open it, while the other robber in the FedEx get-up tapes the older man’s mouth, the video shows.

The surveillance video was first posted on Reddit and police say they’re working on obtaining it.

“Somebody knew something here. There was a setup,” Baxter said, noting that the suspects carried hand-held two-way radios.

The victims, who refused to comment on the matter to The Post, moved to the block one to two years ago and own a city restaurant and karaoke bar, according to neighbors.

“It’s just traumatizing to an 80-year-old couple,” Baxter said. “I mean, they got to sit there and be tied up. What the hell? What are an 80-year-old couple going to do to you.”

No arrests have been made.