concurrency, orthocenter, midpoints, diameters of circumcircle related
Source: Moldova JBMO TST 2013 1.3
July 10, 2020
geometrycircumcircleorthocenterconcurrencyconcurrent
Problem Statement
The point is the center of the circle circumscribed of the acute triangle , and is the point of intersection of the heights of this triangle. Let be the points diametrically opposed to the vertices respectively of the triangle, and be the midpoints of the segments respectively . Prove that the lines are concurrent .