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Kate Middleton Had Private Lunch with King Charles Before Cancer Announcement: They Have a 'Very Good Bond'

The Princess of Wales and King Charles have both recently been diagnosed with cancer

<p>Samir Hussein/WireImage (2) </p> Kate Middleton, King Charles

Samir Hussein/WireImage (2)

Kate Middleton, King Charles

Kate Middleton and King Charles shared a private lunch shortly before the Princess of Wales announced her cancer diagnosis, PEOPLE understands.

The Princess of Wales, 42, and her father-in-law the King, 75, had both already begun treatment for cancer when they met up for lunch last Thursday — ahead of Kate revealing this week in a personal video message that she had been diagnosed with the disease.

With Charles’ treatment beginning on Feb. 5 and Kate’s also underway too, they share “a common health experience” a royal source points out.

Princess Kate and King Charles also share common interests, and Charles "has always had a very good bond with her," according to author Sally Bedell Smith, who recently released her book, George VI and Elizabeth: The Marriage That Saved the Monarchy, in 2023.

"She’s interested in artistic things and she appreciates art and culture so has an affinity with the King over that," Smith tells PEOPLE.

"Obviously they have this in common and can only bring them closer. It is a source of reassurance and consolation for both of them," the author adds.

Related: Kate Middleton Receives Emotional Message from Girl, 8, Who Met the Royal During Her Own Cancer Treatment

<p>Jane Barlow/WPA Pool/Getty; Visionhaus/Getty</p> King Charles, Kate Middleton

Jane Barlow/WPA Pool/Getty; Visionhaus/Getty

King Charles, Kate Middleton

Meanwhile, the King is "progressing well" through his ongoing treatment, PEOPLE has been told.

A royal source adds that they are planning for a summer diary of events without "committing to anything" and that everything will be "subject to doctors' advice at the time."

It's been over a month since Buckingham Palace revealed the King's diagnosis on Feb. 5. His type of cancer has not been disclosed.

At the time, the Palace shared that King Charles had "commenced a schedule of regular treatments, during which time he has been advised by doctors to postpone public-facing duties." The King personally informed his sons, Prince William and Prince Harry, of his diagnosis, as well as other members of the royal family.

<p>Samir Hussein/WireImage</p> King Charles III leaves a national service of thanksgiving and dedication to the coronation of King Charles III and Queen Camilla in July 2023

Samir Hussein/WireImage

King Charles III leaves a national service of thanksgiving and dedication to the coronation of King Charles III and Queen Camilla in July 2023

Related: King Charles Informed of Kate Middleton's Cancer Diagnosis as He Also Undergoes Treatment for Cancer

PEOPLE also understands that earlier in the year, the Princess of Wales and the King were able to meet up in the hospital when they crossed over at The London Clinic for a few nights in January. At the time, King Charles was undergoing a procedure for an enlarged prostate, while Kate was having "planned abdominal surgery."

On Friday, the Princess of Wales shared her cancer diagnosis when she announced in a video message that, following her abdominal surgery, which she said was "successful," later "tests after the operation found cancer had been present." The princess explained that she is currently undergoing preventative chemotherapy.

Princess Kate added that she and her husband Prince William "have been doing everything we can to process and manage this privately for the sake of our young family. As you can imagine, this has taken time. It has taken me time to recover from major surgery in order to start my treatment."

The royal couple share three children: Prince George, 10, Princess Charlotte, 8, and Prince Louis, 5. Kate explained in her video message that it has "taken us time to explain everything to George, Charlotte and Louis in a way that is appropriate for them, and to reassure them that I am going to be OK."

"As I have said to them; I am well and getting stronger every day by focusing on the things that will help me heal; in my mind, body and spirits," she said.

Following an outpouring of support for the Princess of Wales and her family, a Kensington Palace spokesperson on Saturday said in a statement that, "the Prince and Princess are both enormously touched by the kind messages from people here in the U.K., across the Commonwealth and around the world in response to Her Royal Highness’ message."

"They are extremely moved by the public’s warmth and support and are grateful for the understanding of their request for privacy at this time," the spokesperson continued.

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