2016 OIM Problems/Problem 3
Problem
Let be an acute triangle whose circumcircle is . The tangents to through and intersect at . On the arc that does not contain , we get a point , different from and , such that the line cuts the line at . Let be the symmetric point of with respect to the line , and the point of intersection of the lines and . Let be the midpoint of and be the point where the line parallel by to the line intersects the line . Show that the points and are on the same circle.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.