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• Swiatek and Raducanu help Poland, Great Britain advance at Billie Jean King Cup Finals

  Iga Swiatek and Emma Raducanu were both victorious as Poland and Great Britain won their first-round ties at the Billie Jean King Cup Finals on Friday.

  Poland won both of their singles matches against Spain in Malaga, while Britain did likewise versus Germany to seal their own spot in the competition's last eight. 

  World number two Swiatek clinched Poland's progress with a 6-3 6-7 (6-8) 6-1 victory over Paula Badosa, after Magda Linette had put them ahead by beating Sara Sorribes Tormo in a gruelling three-hour, 51-minute affair.

  Speaking after her own win, Swiatek hailed the endurance of team-mate Linette, who triumphed 7-6 (8-6) 2-6 6-4.

  "I wouldn't say that I pushed us to the quarter-finals, because Magda pushed us to the quarter-finals, so we did it together," the five-time grand slam champion said.

  "I'm glad that we won a match as Team Poland. I felt like it was my best match since the US Open. I knew that I could come back in the third set and try to win it for Poland."

  Later on Friday, Great Britain were propelled to victory by Raducanu and Katie Boulter, both of whom were straight-sets victors.

  Raducanu, playing her first match in almost two months after recovering from a foot injury, beat Jule Niemeier 6-4 6-4.

  The 2021 US Open champion started well and her effective serve was a key feature of the opening set, though she later required six match points to get over the line as Niemeier refused to go down without a fight.

  Britain will face defending champions Canada in the last eight after Boulter raced to an impressive 6-1 6-2 victory over Laura Siegemund, ensuring there was no need for Olivia Nicholls and Heather Watson to team up for a deciding doubles match.

• ATP Finals: Perfect Zverev downs Alcaraz to reach semi-finals

  Alexander Zverev has booked his place in the ATP Finals semi-finals with a straight-sets win over Carlos Alcaraz, who is now facing elimination.

  The German secured the year-end number two spot in the ATP rankings after triumphing 7-6 (7-5) 6-4 in just under two hours to set up a meeting with Taylor Fritz in the final four.

  Zverev has now won each of his last eight matches and topped the John Newcombe Group but had to work hard for it, with Alcaraz successfully defending a set point to force a tie-break.

  The Spaniard struggled to match the pace in the second set though, losing his serve in the opening game, giving Zverev the control he needed to register his sixth career win against Alcaraz.

  Zverev avenged his French Open final loss to Alcaraz earlier this year, racking up his 69th win of 2024 in the process, but played down talk he is playing the best tennis of his life.

  "You guys need to relax a little bit," he said. "It has been three fantastic matches. I'm happy to be 3-0 in the group for sure, but the semi-finals now are going to be very difficult - no matter who I am against.

  "Taylor beat me the last few times we've played at the slams, but I'm looking forward to that match.

  "Carlos has beaten me too many times this year in important matches, so I'm happy I got this one. We have a pretty good rivalry, but a great friendship as well. It's always great to share the court with him."

  Alcaraz's chances of qualifying for the final four are slim, but he could progress based on the percentage of games won if Andrey Rublev beats Casper Ruud in straight sets later on Friday.

  Data Debrief: Out in front

  Zverev is looking to cap 2024 on a high by continuing his impressive run, and he is the first player to register 69+ wins in a single season since Andy Murray (78) in 2016.

  Since he made his first semi-final at the ATP Finals in 2018, only Novak Djokovic (five) has reached the semis of this event more often than the German (four).

• Kyrgios confirms return to competitive tennis in Brisbane

  Nick Kyrgios confirmed he is returning to competitive tennis at the Brisbane International at the end of December.

  The Australian announced in October that he was planning to return at the World Tennis League event in Abu Dhabi.

  Kyrgios has played just one ATP Tour singles match in the last two years, having suffered with wrist, knee and foot injuries that have kept him off the court.

  That lone outing came in Stuttgart in June 2023, where he suffered a straight-sets defeat to Wu Yibing.

  "Honestly, this is probably the best I've felt in two years," Kyrgios told Australian television channel 9News.

  "I played that amazing year in 2022. Then, at the finals in Wimbledon and the US Open, that's when I started feeling some issues in my wrist. I had that wrist reconstruction, and now I'm feeling amazing.

  "It was a 15% miracle chance that I was going to get back to playing at this level and here we are.

  "To get back out there in front of the home fans is going to be sick."

  Kyrgios previously won the Brisbane International in 2018 and will be making his fourth appearance at the tournament as he steps up his preparation for the Australian Open.

  He previously said he was aiming for a grand slam title when he returns, having lost his only previous such final to Novak Djokovic at Wimbledon in 2022.

  "I am feeling fit and healthy, and I am excited for my return to tennis following some time out of the sport," Kyrgios added.