2021 OIM Problems/Problem 2
Problem
Consider an acute triangle , with , and let be its circumcircle. Let and be the midpoints of the sides and , respectively. The circumcircle of triangle intersects at and , with . The line and the line tangent to at intersect at . Let be the point on segment such that , with , and let be the point where intersects the line parallel to passing through . Show that is the midpoint of .
Note: The circumcircle of a triangle is the circle passing through its three vertices.
Solution
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