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It is billed as the Greatest Show on Earth.

But the glitz and glamour of the Olympics is taking place against a backdrop of a city gripped by violence, vice and crime.

Even as billions tuned in to see the action this week, three men – suspected gang members who rule the city’s favela slums – were shot dead by cops in a gun battle in north Rio.

A patrol of the 85,000-strong security forces brought in for the Games were shot at in the Mare favela after taking a “wrong turn”.

And within walking distance of the Olympic Park, where British stars Mo Farah, Greg Rutherford and Jessica Ennis-Hill are taking centre stage, underage girls sell their bodies, in a city with 12,000 sex workers.

In the infamous Vila Mimosa – City of Tender Love – prostitutes made fliers for the Games, offering “cut-price” sex for 40 reals, or £9, almost half the usual price of 75 reals, or £17.

(Image: Andy Stenning / Daily Mirror) (Image: Andy Stenning / Daily Mirror) (Image: Andy Stenning / Daily Mirror)

Vila Mimosa, Rio’s oldest and largest prostitution zone, where 3,000 women offer their services in more than 70 bars, has been hit by the deepest recession in a century.

A flyer printed in English states that an hour’s sex during the Games will cost 60 reals (£13), down from 90 reals (£20), while a threesome is priced at 40 reals (£9) per girl for half an hour, and 80 reals (£18) for an hour.

But even with discounts, the trade has not been what they expected. It was the same for the World Cup two years ago, when visitors were put off by the prospect of being mugged.

Rio has seen a steep rise in violent crime recently, with 2,000 murders in the first seven months of this year.

Militias now run the litter-covered favela, in the west zone of the city, where the poor ended up after they were evicted from their homes for the Games.

This, and the battered economy, has seen many women end up working as prostitutes, say charities.

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(Image: Andy Stenning / Daily Mirror) (Image: Andy Stenning / Daily Mirror)

It is legal for over-18s, but illegal to be a pimp.

In Vila Mimosa, a mile from the Maracana Stadium, worker Tatiane tells how she has learnt to say: “Hello baby, want something tasty?... Let me show you a good time.”

With a dragon tattoo on her back, ­turquoise eye-shadow, a belly ring and the bare essentials covering her up, the mum sees 15 to 20 clients every Friday, Sunday and Monday, from 3pm to 9am.

She takes clients upstairs via a spiral staircase at the back of the bar she operates from, and into a cell-like room with a single bed, stool and bin.

Tatiane’s husband thinks she is a bar manager.

(Image: Andy Stenning / Daily Mirror) (Image: Getty) (Image: Getty)

She told the Sunday People: “He’d kill me if he found out. I like doing this. It’s easy money.

"I will be targeting English men – I hear they like us sexy Brazilian women.”

Around Copacabana beach, prostitute Juliana uses Facebook and Tinder to attract Westerners.

She says: “It is the ambition of all the girls here to be with an Olympic athlete.”

But tellingly, she adds: “The Olympics are an opportunity to meet nice people with money and perhaps escape… leave this life behind.”

(Image: Reuters) (Image: Getty)

Outside the city – 50 minutes from Rio’s Olympic Village – girls as young as nine are used by truckers for sex.

The BR-116 road runs to Sao Paulo, where the Arena Corinthians will stage Olympic football games.

But its real misery occurs at 262 truck stops along its way. Traffickers target poor families on the route, offering money for their girls.

Matt Roper, an ex-Daily Mirror journalist whose Meninadanca charity helps victims, said: “Before the Games, a brothel specialising in underage girls right in front of the Olympic Park was busted.

"We don’t know how many others have escaped the police radar.”

The Olympics are estimated to have cost at least £7billion, sparking protests by impoverished locals.

And Matt says rather than sporting glory, it is child exploitation that could be the Rio Games’ big legacy.