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It was not even a show of modesty from Korda but a reflection of the sporting success his parents and siblings have achieved.

The 22-year-old American has had big wins before, yet his 7-6 (9-7) 6-3 7-6 (7-4) win against 2021 US Open champion Medvedev on Rod Laver Arena might go down as the best of the lot. It was his first win over a top-10 player in a grand slam and means Medvedev will slide out of that elite group at the end of the tournament.

Korda has made an outstanding start to the year, defeating Andy Murray and Jannik Sinner on his way to the Adelaide International 1 final, where he took a set off Novak Djokovic.

Now he is through to the fourth round of a Major for a third second time after previous runs at the French Open and Wimbledon.

Reminded about his father Petr's Australian Open men's singles title in 1998, Korda stepped in to say: "Even better, though, my sisters won the Australian Open in women's golf."

LPGA Tour stars Jessica and Nelly Korda took that title in 2012 and 2019, respectively, on the way to being recognised among the biggest stars in their sport.

Mother Regina was also an established tennis player on the WTA circuit in the 1980s and early 1990s.

"I don't know what I'm going to be ranked. My mum's career-high was number 24, my dad was two," Korda said.

"Nelly, my sister was number one, my older sister Jessica was six, so I'm definitely the worst athlete in the family so far."

As it stands, Korda has moved to No.28 on the provisional ATP rankings by coming through three rounds.

He won the Australian Open boys' title in 2018 but now has bigger targets, with a fourth-round tussle against Hubert Hurkacz ahead of him.

Korda has Andre Agassi in his corner, albeit distantly. He has described the four-time Australian Open winner as a "mentor", and Las Vegas-based Agassi stayed up until the early hours at home to watch the Medvedev match.

"He texted me. He's going to bed now," Korda said after his late-night win in Melbourne.

"He's one of the most special people in my life. We started talking during COVID in 2020. He's been one of the biggest parts in my rise. Just overall as a tennis player, as a human being. We spend a lot of time together. He's very special to me."

Now No.10 seed Hurkacz awaits, and Korda, No.29, knows that will be a tricky assignment.

"We practise quite a bit," Korda said. "Usually whenever we practise, he actually wins the tournament. I always give him jokes about that. I'm looking forward to it. It's exciting, the fourth round of a grand slam. I'll be ready to go."

Can Korda win the Australian Open, just like his dad, and keep up the family tradition of outstanding results in the country?

"It's a special place for us," he said. "We've had some really great results. Hopefully I can do one better than the juniors and do it in the pros."