Eloise Dixon and her family were holidaying in the seaside resort of Angra dos Reis when they took a wrong turn Sunday while looking for a place to buy water and entered the slum, according to Brazilian media oganisation O Globo.
Inside the favela, called Agua Santa, "they were confronted by criminals who ordered them to get out and the car was hit by shots from a firearm," local police chief Bruno Gilaberte said.
The woman underwent surgery in the Angra dos Reis hospital and "is in stable, good condition," he said.
According to Brazilian media reports, the woman was due to be transferred to a Rio hospital Monday.
"The bullet went through the whole abdomen but by luck didn't hit major arteries or important organs. She was really lucky," local hospital director Rodrigo Mucheli said on Globo television.
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Television footage of the damaged rental car showed how close an escape the British visitors had: one bullet hit a front tire, another the front passenger door and a third the headrest where the victim was sitting.
The Rio area is one of the world's most famous tourist destinations but many favelas -- largely unregulated communities of working class Brazilians -- are effectively no-go areas for outsiders and even for police.
Vinicius Barbosa, the deputy chief executive of the Angra dos Reis government, condemned the authorities' lack of control over high-crime areas "where you can't go in, where the media can't go in, where services can't go in -- this is intolerable."
Rio de Janeiro has become so violent this year in the aftermath of the 2016 Olympic Games that the federal government sent thousands of army troops in July to support police.
