MathDB
concurrency, orthocenter, midpoints, diameters of circumcircle related

Source: Moldova JBMO TST 2013 1.3

July 10, 2020
geometrycircumcircleorthocenterconcurrencyconcurrent

Problem Statement

The point OO is the center of the circle circumscribed of the acute triangle ABCABC, and HH is the point of intersection of the heights of this triangle. Let A1,B1,C1A_1, B_1, C_1 be the points diametrically opposed to the vertices A,B,CA, B , C respectively of the triangle, and A2,B2,C2A_2, B_2, C_2 be the midpoints of the segments [AH],[BH]¸[CH][AH], [BH] ¸[CH] respectively . Prove that the lines A1A2,B1B2,C1C2A_1A_2, B_1B_2, C_1C_2 are concurrent .