2019 OIM Problems/Problem 3
Problem
Let be the circumcircle of triangle . The parallel to that passes through cuts at () and the parallel to that passes through cuts at (). The straight lines and intersect at , and lines and intersect at . Let be the midpoint of . The line cuts at () and the line at . The line cuts the circumcircle of triangle at (). If the lines and intersect at , show that belongs to the line .
Note: The circumcircle of a triangle is the circle that passes through the vertices of the triangle.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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