The Princess of Wales has presented the Wimbledon men’s final trophy to Carlos Alcaraz, in her second public engagement since announcing her cancer diagnosis.

Kate, patron of the All England Lawn Tennis and Croquet Club, spoke to ball boys and girls after she entered Centre Court to loud applause on Sunday afternoon.

Before passing the trophy to Alcaraz, Kate commiserated and shook the hand of runner-up Novak Djokovic.

Kate, wearing a purple Safiyaa dress, attended Sunday’s final with her daughter, Princess Charlotte, and her sister Pippa Matthews.

A photograph posted on Wimbledon’s X account showed Charlotte shaking the hand of Alcaraz as he held the trophy inside the championship’s grounds.

Kate and Charlotte were greeted by British players Emma Raducanu, Sonay Kartal, Lily Miyazaki, Lucy Shuker and Flora Johnson as they arrived on the players’ lawn at Wimbledon before entering Centre Court.

Charlotte gave wheelchair tennis player Shuker a “pinky promise” that she would try the sport alongside her mother.

Kate was also introduced to Raducanu, who was knocked out in the fourth round of this year’s championships, telling her: “It was so hard to see you go out.”

US Open winner Raducanu said it was “amazing” to have the support of the princess and “see her here looking so healthy and happy”.

Kate and Charlotte were greeted with cheers and applause as they took their seats in the front row of the royal box at Centre Court.

The Princess of Wales smiled broadly and waved to the crowd as the pair sat down beside her sister Ms Matthews.

Actors Tom Cruise, Benedict Cumberbatch and Julia Roberts were among the other famous faces in the royal box for Sunday’s final.

While meeting the players, Kate said Charlotte, who was wearing a navy polka dot dress, had been “practising yesterday” and that tennis was “really great for the youngsters”.

Kate said she had been “filling in the leaderboard” with Charlotte during Wimbledon, adding: “As a family, we play a lot.”

After being asked to try wheelchair tennis by Shuker, Kate said: “I’ve tried wheelchair rugby before, but not tennis. You’ll have to hold me to that.”

Shuker, the highest ranked British wheelchair women’s tennis player, told the PA news agency: “She was just saying how amazing it’s been to watch and follow everyone’s career.

“Alfie Hewett won the men’s wheelchair tennis earlier. I just asked if they were playing tennis themselves, which they have been, and then said: ‘Have you tried wheelchair tennis?’

“And I got a little pinky promise from Princess Charlotte that she would try it.”

Shuker added: “For me, it’s incredibly humbling to be here and to be asked to meet the princess today.”

Discussing her meeting with Kate, Raducanu told PA: “It was very nice to see Her Royal Highness again. I’ve met her twice before, and it was really nice to meet Charlotte as well, because I hadn’t before.

“It’s amazing to see her be such a champion of tennis and following all of us.

“We just spoke a little bit about my tournament, and the tennis, and also how I missed last year but I was very excited to come back this year. And a little bit about her tennis because she loves it.”

Asked about Kate’s appearance at the tournament following her diagnosis, Raducanu said: “I think it just shows her resilience and how much of a role model she is and it’s amazing to see her here looking so healthy and happy.”

Wimbledon wildcard entry Miyazaki said it was “really special” to meet the royals.

Asked about meeting Kate, Miyazaki told PA: “She’s had a really tough time and it was great to see her looking healthy.

“It’s special to have that support from the royal family and it’s really cool to know that they are tennis fans.”

Before entering Centre Court, Kate also met people who had worked at this year’s championships.

Emmanuela Asamoah, a worker in the Wimbledon general office, said it was “insane” to meet Kate and Charlotte, who she described as “really lovely people”.

Discussing her meeting with Kate, Ms Asamoah, 18, told the PA news agency: “She asked us a lot about our well-being first, which I found just so heartwarming.

“She introduced us to Princess Charlotte, which was so sweet.

“They were just really lovely people in general. I couldn’t have asked for a nicer introduction to her.”

Kate has been undergoing chemotherapy and made her first public appearance since announcing her cancer diagnosis in March at the Trooping the Colour ceremony in London last month.

She did not attend the women’s singles final on Saturday, and Wimbledon chairwoman Debbie Jevans presented the trophy to Barbora Krejcikova on her behalf.

During their meeting on Sunday, Krejcikova gifted the Princess of Wales the racquet she used during her victory.

Actors Tom Cruise, Zendaya and Hugh Jackman were among the celebrities attending Centre Court as Czech player Krejcikova fought off Italian Jasmine Paolini to claim a 6-2 2-6 6-4 victory.

Earlier in the tournament, Kate paid tribute to double champion Sir Andy Murray, saying he should be “so very proud” after he missed out on a final chance at Wimbledon.

In a personally-signed message on social media, the princess wrote: “An incredible #Wimbledon career comes to an end. You should be so very proud @andy_murray. On behalf of all of us, thank you! C.”

Kate visited the championships several times last year and presented Alcaraz with his first Wimbledon trophy after watching him battle Djokovic in the men’s singles final.

On Friday, Kate missed a charity polo match as husband William took to the field to raise funds for good causes at Guards Polo Club in Windsor Great Park.

In a statement released last month, the princess revealed she is making good progress but “not out of the woods yet” and has “good days and bad days” as she continues her treatment.

The Prince of Wales, president of the Football Association, will be in Berlin later on Sunday to attend England’s Euro 2024 final against Spain.

Some spectators at Wimbledon could be seen wearing white England football shirts at the championships on Sunday morning.