Really? this question was asked in an actual competition?

Yes, I know it's easy. Keep in mind that Puerto Rico only has a population of about 3.5 million and the education system is not great, which both limit the amount of competitors we have in math competitions, which limits how difficult the problems can be. Additionally the time we get to the final selection test we have about 8 people each from grades 7 to 12. If they make the test too hard the younger kids could get discouraged and not want to continue the olympiads, so we want to make sure the test is at least manageable for everyone.

Don't play it down so much Over the years, Puerto Rico had silver and gold medals at the IMO, and sported such luminaries as Sherry Gong.

I am aware. But they need to have at least some easy questions on the test. Also note that usually the top of the pile is decided by how many mistakes you made since usually the best students can solve most or all of the problems.

Are you permitted to just say that this is true by Vivani's.

No this question is asking for a proof of the fact.

Lol I have seen this question in an Olympiad in my 7th grade, and in my school's assignment in 8th grade

I developed a geometric induction solution to this that was like three pages before I realized that the solution was an area proof that could be put in a tiny paragraph...