Скачать или смотреть Euclidean Geometry (Question 6)

I don't know. This question has a habit of getting viral on social media (especially Facebook) at least once in a year ..... or at least it seems so, according to my news feed.

This question is from the book "Challenging Problems in Geometry" by Alfred Posamentier and Charles Sarkind. The solution I am discussing is basically how the book solved it. I would have loved to give my own solution, and I tried using the coordinate approach. That made things worse. Also, I had to use approaches similar to the one shown in the video to make things simple. So, the use of coordinate system was pointless. And I don't think there's a solution which is simpler than this.

It has been discussed by many people, and has been solved on YouTube platforms as well. But I have seen some of them credit themselves for coming up with the question, while many never mentioned the source. They're also using the book's solution, none of them (or at least the ones I came across) have given their own solution. I feel that's very wrong. That's the main reason why I felt like discussing this question, even though I didn't have anything new to offer than some "observations" which made the discussion slightly more rigorous.