1:56 PM PT -- A rep for the Teenage Cancer Trust -- an org that Kate has worked with in the past, before her cancer diagnosis -- tells TMZ ... "Our thoughts are with Her Royal Highness the Princess of Wales, and we wish her all the best for her treatment."

They add, "If you think you have cancer yourself, it’s important to get checked out as soon as you can."

12:11 PM PT -- King Charles is extending his well-wishes to Kate Middleton during her cancer battle, with Buckingham Palace saying, "His Majesty is so proud of Catherine for her courage in speaking as she did."

They go on to say that after Kate's hospitalization, Charles has "remained in the closest contact with his beloved daughter-in-law throughout the past weeks." BP continues, noting Their Majesties "will continue to offer their love and support to the whole family through this difficult time."

Kate Middleton just announced she has cancer -- breaking her silence on months of speculation over her health ... and it sounds serious.

The Princess of Wales showed face Friday in a video that Kensington Palace posted -- and in it, Kate addresses the public ... revealing she was diagnosed with cancer, something that was discovered after her abdominal surgery in January.

Kate says, "In January, I underwent major abdominal surgery in London and at the time, it was thought that my condition was non-cancerous. The surgery was successful. However, tests after the operation found cancer had been present. My medical team therefore advised that I should undergo a course of preventative chemotherapy and I am now in the early stages of that treatment." She didn't address the specific type of cancer she's battling.

Kate also appears to allude to her lengthy absence, as she says she and Will have needed time to address this health issue with their three children -- all of whom are fairly young -- as she's wanted to assure them that she's going to be okay.

We broke the story, Kensington Palace was geared up to provide a major update on Kate's health -- something they've now done, and it's left many heartbroken as Kate battles this.

In her video, Kate asks for privacy during this difficult time as she undergoes chemotherapy.

The announcement ends months of speculation over Kate's whereabouts and health -- which kicked off in mid-January when the Princess of Wales was hospitalized for abdominal surgery ... a hospitalization that came out of nowhere, and which was supposed to end in 2 weeks.

Obviously, Kate was out of the public eye for way longer than that ... and the longer it went on, the more they pedaled conspiracy theories and fueled a never-ending rumor mill.

At first, all the talk and gossip about Kate started as relatively light -- namely, through a bunch of memes and jokes online ... where people poked fun about the situation -- but which only grew in seriousness the more that the Palace attempted to address all the conjecture.

At first, the Palace just issued a statement -- saying Kate was still recovering and doing well ... and then, not long after, we saw Kate surface in public for the first time ... showing up in a car being driven by her mother, where Kate was wearing shades and maintaining a low profile.

People didn't buy that was Kate, and the memes and jokes only continued -- with the conspiracy theories kicking into overdrive. After that, the Mother's Day photo fiasco occurred.

Remember -- Kensington Palace posted a picture that they said had been taken by Prince William .... showing Kate with her kids. However, it quickly became clear that the image had been doctored in Photoshop -- with several apparent alterations having occurred in editing.

Kate put out a statement in the aftermath of that ... copping to the fact she edited it.

Fast-forward to last weekend, when Kate and William surfaced at a farm shop about a mile from their home -- which became the first true sighting of Kate out and about on her own two feet. While she looked happy and fairly healthy ... many noticed her weight loss.

The cancer news now clarifies why Kate appeared so thin in our video -- she's in treatment for it ... and this is one of the known side effects, and it can take a heavy toll on the body.

This update is clearly devastating for her family and loved ones -- but also, for all of the UK as well ... of which she serves as a key Royal figure, and which she's served dutifully.

It also goes without saying ... Kate is now the second senior Royal to be battling cancer. Her father-in-law, King Charles, was also recently diagnosed with cancer -- although it's unclear what form he has, or at what stage it is. With that said, Charles has been carrying on with his duties of late.

Tough times for Kate and the Royal Family at large ... best wishes to her and all of them.