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Helicopter tours depart from a helipad on Urca Mountain for short but unforgettable views of one of the world's most scenic cities.

Standing near the precipice of Pedra Bonita, 696 metres above Rio, I watched a young woman from Hungary run to the edge and leap into thin air.

Gone. Dropped like a stone. I could see the beach far below as a distant smudge, and apartment towers that looked like Monopoly tokens – but where was the girl?

Then, she rose up, goddess-like, her bright yellow hang glider riding an updraft. She and her tandem pilot drifted calmly into the blue. The next kite was pulled into place, like a plane on a runway.

"Mel!" called a pilot to my friend, whose number was up. "Let's go."

Mel was visibly shaky. "This isn't what I thought you meant when you promised to show me the high spots of Rio," he said.

Okay, so I'm literal. I'd been to Rio de Janeiro a few times before and didn't want my buddies to miss any of the highs the "Marvellous City" has to offer, physical or emotional. Hang-gliding above one of the world's most beautiful urban geographies tops the list.

There are a few gliding outfits to choose from, and we went with Rio Hang Gliding, run by an international champion glider named Konrad Heilmann.

"Two things to remember," he said, clipping my harness and his to the kite in a crash course that took all of five minutes. "Don't touch the bar." It controls the kite. "And don't stop running." To chicken out at the edge of the wooden ramp while your pilot keeps running could have disastrous consequences.

I glanced at the wind sock, hanging limp.

"Run!" Konrad barked, and we barrelled across the boards until my legs were paddling air like a cartoon character. Initially, we dropped – winds were light – but suddenly, the kite climbed, wheeled, circled. I was euphoric.

I was soaring like a bird, without sound or effort, taking in Rio's spectacular views.

We circled over the ocean, a highway, expensive hillside homes and plopped neatly onto Sao Conrado beach seven minutes later. I didn't want it to end. Even with my feet on the sand I still felt I was soaring

Rio is gifted with a unique topography of abrupt granite domes surrounding sweeping bays. The unusual mountains are called bornhardts, after a German geologist, formed when pools of magma cool and crystallize beneath the earth's surface under uniform pressure. Tectonic shifts shoved them high into the air.

Pedra Bonita, our launch site, is just one of many such mountains. Nearby is another, Morro Dois Irmaos, standing like a sentinel over the western end of Ipanema beach, iconic for its twin peaks (its name means "two brothers"). The taller of the two was the next stop on our tour.

A public bus dropped us at the entrance to a favela called Vidigal, a poor slum climbing the steep mountainside. The trail head for the easy three-hour hike lies at the top of the favela, so we hired moto taxis driven by suicidal teenagers to take us there. Since it's been pacified by police who won control from drug gangs, Vidigal offers the opportunity to witness favela life without much danger. Except for the motorcycle ride, that is.

Maniacally dodging people, vans, chickens and dogs, the lift to the trail head was every bit as exciting as the hike itself.

We found a dirt path that wends through forest, here and there offering dizzying views of another favela, Rocinha, Rio's largest. We emerged onto bald rock and soon we were at the top, taking in a picture-perfect vista: the full sweep of the Leblon and Ipanema beaches, the inland lake called Lagoa Rodrigo de Freitas and the surrounding mountains.

The most famous and tallest example of Rio's bornhardts is Corcovado (Portuguese for hunchback), at 733 metres the ideal pedestal on which to perch a statue of Christ the Redeemer. Ascending to the statue can be done in a funicular tram, but you'll have to line up for hours. From the funicular station (reached by any bus from the city-designated Cosme Velho), you can also catch a minibus transfer up the mountain, which is faster. Like fools, we walked.

The ascent snakes through a piece of the Tijuca rainforest, some of the last surviving Atlantic rain forest in the world. At the top, the observation deck is a mob scene of selfie-snapping tourists, but the reward is worth it: The ultimate view of Rio, the one in all the postcards, featuring another Rio icon front and centre: Sugarloaf Mountain.

That granite dome, Sugarloaf, guarding the entrance to Guanabara Bay, was our next stop. Most say Corcovado offers the best view of Rio, but I think the views from Pao de Acucar, as Sugarloaf is known in Portuguese, are the prettiest. And I love the cable cars. My tip to visitors is to time your visit for late afternoon so you can see the daylight view, the sunset view (with the sun going down behind Corcovado) and night views.

Reaching this Rio high point requires two cable-car rides. The first ascends to the top of a smaller granite hill called Urca (220 metres) where you transfer to the second car and slide skyward toward Pao de Acucar itself (396 metres).

Cable cars have been making this journey since 1912. (Not the same ones; today's cars are high-tech and inspected daily.) If you're up for it, a walking trail leads to the top of Urca, clearly marked. The half-hour walk is a nice opportunity to spy the mischievous marmosets (monkeys the size of squirrels) and the brilliant red Brazilian tanager. And then you'll only need to buy half a ticket to ride the aerial tram from Urca to Pao de Acucar's summit.

While waiting to transfer atop Urca, we noticed another way to get high. Helicopter tours are normally out of my budget, but the chance to buzz around the world's most breathtaking city was irresistible. Flight tour operator Helisight maintains a helipad on Urca, and anyone can hop on for a ride without reservations. All that's required is a minimum of three people and a credit card. The three of us ponied up about $150 each for a seven-minute thrill ride. Like the hang-glide, it's a short trip that lives large in my memory.

For a few days in Rio, we were walking on air, so to speak. To toast our high-flying lifestyle, we capped our visit with a stop at the rooftop bar of the Rio Othon Palace, the tallest hotel on Copacabana Beach. Sipping Brahma beer, looking out over the richly hued panorama of beach, city and sea, we tried to prepare mentally for a return back to earth.

Re-entry would be difficult.

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