An Olympiad Geometry Problem Solved Using Radical Axes
<p>This problem is quite hard (or maybe even impossible) to solve using elementary Geometry techniques, such as angle chasing. Therefore, we present a solution that uses the properties of the radical axes and their intersection — the radical center. If you are unfamiliar with those terms, I recommend you reading the second chapter of Evan Chen’s <em>Euclidean Geometry in Mathematical Olympiads</em>.</p>
<p>Our goal is to prove that four points lying on two circles are concyclic. This might immediately remind you of the theorem about the radical center. Here it is, in case you have forgotten about it:</p>
<p><a href="https://medium.com/intuition/a-geometry-problem-solved-using-radical-axes-77b2dbbc282e"><strong>Website</strong></a></p>