Another “Radical” Geometry Problem from IMO

As always, try solving this problem for yourself, before reading the solution. Even though this is an IMO problem, you still might be able to solve it, don’t give up too easily, and remember that it is always recommended to work on such problems for at least a few hours. Even if you don’t manage to solve it, you still might learn something new and gain experience. <h1>Solution</h1> This problem can be surprisingly easily solved using the properties of the radical axes, namely, the theorem about the radical center. If are unfamiliar with those terms, I highly recommend reading the second chapter of Evan Chen’s Euclidean Geometry in Mathematical Olympiads, or any other source that you can easily find on the Internet. Radical axes have a lot of applications in Olympiad Geometry, so make sure to study them thoroughly. <a href="https://medium.com/intuition/another-radical-geometry-problem-from-imo-5978d37a126d">Learn More</a>