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The Bulgarian, who reached the Australian Open semi-finals and claimed his maiden ATP Masters 1000 title in Cincinnati in 2017, staked his claim as a contender to progress from Group Pete Sampras with an enthralling win.
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Dimitrov failed to serve out the match at the first time of asking, only for Thiem to hand him a second opportunity with two double faults in a row.
The Bryans broke serve at the end of the first set to clinch it 7-5 before taking an early lead in the second.
The 26-year-old earned a break point on Thiem's first service game but let the Austrian off the hook with a backhand into the net. "We fought hard to come back in the second set".
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The film, which was already completed and set for release before the end of the year, remains on track for a December 22 premiere. The actor is pleased with the role, sharing, "I'm fascinated by doing real people". "I'm used to big roles and lots of words".
"I'm not going to lie - I was pretty nervous, my first match out here", he told reporters.
Both players began the encounter hitting the ball crisply from the baseline but Thiem was the first to be broken in the sixth game of the match and Dimitrov maintained the advantage to close out the opening set without facing a single break point.
And Dimitrov finally triumphed after two hours and 22 minutes, serving out victory via a nervy deuce.
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Since leaving the White House, Biden has launched the political action committee American Possibilities and the Biden Foundation. The former US senator added, "But who knows what the situation is going to be a year and a half from now".