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Video - King puts GB back in medal contention
Australia's Olympic eventing team, led by a couple who live in Britain, topped the rankings after the dressage stage while Team GB rose to fourth position.
Lucinda and Clayton Fredericks helped the five-strong Australia team push clear of Germany and the United States.
Lucinda was top of the individual standings, with her husband sixth and Mary King the top Briton in ninth.
King, aboard Call Again Cavalier, and Sharon Hunt on Tankers Town did well to keep Britain in medal contention.
It was a fine effort in particular by King, who finished with just 38.10 penalty points in her fifth Olympic Games.
"As long as I ride him well we should have superb rounds," said King of her mount.
Her mark, supported by Hunt on 43.50, meant the team could discount the scores of Daisy Dick and William Fox-Pitt, who had disappointed a day earlier.
They will look to climb up the standings further on Monday when the eventers take on the challenging cross-country at the Beas River course in Hong Kong.
With hot and humid conditions, the course is likely to provide a stern physical and mental challenge.
Medals will be decided on Tuesday with the final leg of the competition, the show jumping final.
Britain's Tina Cook is 13th in the individual standings, five places ahead of Hunt, with Fox-Pitt 34th and Dick 37th.
Lucinda Fredericks set the pace on Headley Britannia, with 30.40 penalty points.
Leading the chasing pack are Belgium's Karin Donckers (31.70) with Gazelle De La Brasserie, and Germany's Ingrid Klimke (33.50) on Abraxxas.
In the team event, Australia led with a total score of score of 102.80, followed by Germany (110.50), the United States (115.60) and Britain (121.80).